样式: 排序: IF: - GO 导出 标记为已读
-
Automorphic Carathéodory–Julia Theorem Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-04-22 Alexander Kheifets
Let \(w(\zeta )\) be a function analytic on \({{\mathbb {D}}}\), \(|w(\zeta )|\le 1\). Let \(|t_0|=1\). Assume that w and \(w'\) have nontangential boundary values \(w_0\) and \(w'_0\), respectively, at \(t_0\), \(|w_0|=1\). Then (Carathéodory–Julia) \(t_0\dfrac{w'_0}{w_0}\ge 0\). The goal of this paper is to obtain a lower bound on this ratio if w is character-automorphic with respect to a Fuchsian
-
Weyl Sets in a Non-degenerate Truncated Matricial Hausdorff Moment Problem Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-04-17 Max Heide, Bernd Fritzsche, Bernd Kirstein, Conrad Mädler
Given a point w in the upper half-plane \(\Pi _{\mathord {+}}\), we describe the set of all possible values F(w) of transforms \(F(z)\,{:=}\,\int _{[\alpha ,\beta ]}(x-z)^{-1}\sigma (\textrm{d}x)\), \(z\in \Pi _{\mathord {+}}\), corresponding to solutions \(\sigma \) to a (non-degenerate) truncated matricial Hausdorff moment problem. This set turns out to be the intersection of two matrix balls the
-
Sequences of Operators, Monotone in the Sense of Contractive Domination Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-04-15 S. Hassi, H. S. V. de Snoo
A sequence of operators \(T_n\) from a Hilbert space \({{\mathfrak {H}}}\) to Hilbert spaces \({{\mathfrak {K}}}_n\) which is nondecreasing in the sense of contractive domination is shown to have a limit which is still a linear operator T from \({{\mathfrak {H}}}\) to a Hilbert space \({{\mathfrak {K}}}\). Moreover, the closability or closedness of \(T_n\) is preserved in the limit. The closures converge
-
Controllability of Mild Solutions for Second-Order Neutral Evolution Equations with State-Dependent Delay Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-04-10 Chahrazed Boudefla, Fatiha Sahraoui, Selma Baghli-Bendimerad
The objective of our research is to demonstrate the controllability of mild solutions for a specific class of second-order neutral functional evolution equations that involve state-dependent delay. To achieve this, we rely on Avramescu’s nonlinear alternative theorem and leverage cosine function theory.
-
$$L\log L$$ Type Estimates for Commutators of Fractional Integral Operators on the p-Adic Vector Space Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-04-09 YunPeng Chang, LiangJuan Yu, LinQi Sun, HuangZhi Xia
In this paper, the main aim is to prove the weak type \(L \log L\) estimates for commutators of fractional integral operators and the higher order in the context of the p-adic version of Lebesgue spaces, where the symbols of the commutators belong to the p-adic version of \({\text {BMO}}\) space. In addition, we also establish the estimates of the sharp function on the p-adic vector space.
-
Hilbert Transform, Nevanlinna Class and Toeplitz Kernels Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-04-07 Arun K. Bhardwaj, Javad Mashreghi, R. K. Srivastava
In this article we obtain an explicit formula for the Hilbert transform of \(\log |f|,\) for the function f in Nevanlinna class having continuous extension to the real line. This family is the largest possible for which such a formula for the Hilbert transform of \(\log |f|,\) can be obtained. The formula is very general and implies several previously known results.
-
b-AM-Dunford–Pettis Operators on Banach lattices Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-04-06 Hamadi Baklouti, Mohamed Hajji, Radhouene Moulahi
In our research work, we introduce a new class of operators that we call b-AM-Dunford–Pettis operators. Properties of b-AM-Dunford–Pettis operators, the relationship between the b-AM-Dunford–Pettis operators and various classes of operators are investigated. On the other side, our techniques and results will be related to the lattice structure of the b-AM-Dunford–Pettis operators. For instance, it
-
C*-Algebras Generated by Radial Toeplitz Operators on Polyanalytic Weighted Bergman Spaces Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-04-05 Roberto Moisés Barrera-Castelán, Egor A. Maximenko, Gerardo Ramos-Vazquez
In a previous paper (Barrera-Castelán et al. in Bol Soc Mat Mex 27:43, 2021. https://doi.org/10.1007/s40590-021-00348-w), using disk polynomials as an orthonormal basis in the n-analytic weighted Bergman space, we showed that for every bounded radial generating symbol a, the associated Toeplitz operator, acting in this space, can be identified with a matrix sequence \(\gamma (a)\), where the entries
-
A Characterization of Invariant Subspaces for Isometric Representations of Product System over $$\mathbb {N}_0^{k}$$ Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-04-03 Dimple Saini, Harsh Trivedi, Shankar Veerabathiran
Using the Wold–von Neumann decomposition for the isometric covariant representations due to Muhly and Solel, we prove an explicit representation of the commutant of a doubly commuting pure isometric representation of the product system over \(\mathbb {N}_0^{k}.\) As an application we study a complete characterization of invariant subspaces for a doubly commuting pure isometric representation of the
-
Blaschke Products and Convolutions with a Slanted Generalized Half-Plane Harmonic Mapping Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-04-03 Stacey Muir
It is known that if the convolution of two suitably normalized planar harmonic mappings from certain families of mappings, such as those mapping into a half-plane or a strip, is locally univalent, the convolution is univalent and convex in one direction. After extending this to convolutions of mappings into a slanted half-plane with those into a slanted asymmetric strip, we prove properties for the
-
On the Submultiplicativity of Matrix Norms Induced by Random Vectors Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-04-02 Ludovick Bouthat
In a recent article, Chávez, Garcia and Hurley introduced a new family of norms \(\Vert \cdot \Vert _{{\textbf {X}},d}\) on the space of \(n \times n\) complex matrices which are induced by random vectors \({\textbf {X}}\) having finite d-moments. Therein, the authors asked under which conditions the norms induced by a scalar multiple of \({\textbf {X}}\) are submultiplicative. In this paper, this
-
A Potapov-Type Approach to a Particular Truncated Stieltjes Moment Problem in the Case of an Odd Number of Prescribed Matricial Moments Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-04-02 Torsten Schröder-Zeiske, Bernd Fritzsche, Bernd Kirstein, Conrad Mädler
The paper gives a parametrization of the solution set of a matricial Stieltjes-type truncated power moment problem in the non-degenerate and degenerate cases. The problem will be reformulated as an interpolation problem for a distinguished class of holomorphic matrix-valued functions. An essential role plays a solution of the corresponding system of Potapov’s fundamental matrix inequalities.
-
Some Approximation Properties of Parametric Baskakov–Schurer–Szász Operators Through a Power Series Summability Method Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-04-01 Naim L. Braha, Toufik Mansour, Mohammad Mursaleen
In this paper, we study some properties of the parametric generalization of the Baskakov–Schurer–Szász operators using a power series summability method. We prove some results in the weighted spaces of continuous functions and the Voronovskaya type theorem. Further, we prove some results related to the statistical convergence of the parametric generalization of the Baskakov–Schurer–Szász operators
-
Infinitely Solutions for a Fractional $$p(\cdot ,\cdot )$$ -Kirchhoff Type Problem Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-30 Abdelhak Mokhtari, Mouna Kratou, Kamel Saoudi
The purpose of this paper is to study the existence and infinitely many solutions for a some type of nonlocal \(p(\cdot ,\cdot )\)-Kirchhoff problems with Dirichlet boundary conditions. Our proofs are based on variational methods, the Mountain Pass Lemma, and genus theory.
-
Analytic Function Spaces Associated with the p-Carleson Measure for the Bloch Space Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-29
Abstract We investigate the p-Carleson measure for the Bloch space \({\mathcal {B}}\) and introduce a holomorphic function space \( W_{\mathcal {B}}^{p,\alpha }\) associated with this measure. An integral operator which preserves the p-Carleson measure for \({\mathcal {B}}\) is established. As applications, we give a generalized Jones’ formula for \( W_{\mathcal {B}}^{p,\alpha }\) , characterize the
-
Annihilators in the Bidual of the Generalized Group Algebra of a Discrete Group Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-27 Lav Kumar Singh
In this short note, the second dual of generalized group algebra \((\ell ^1(G,\mathcal {A}),*)\) equipped with both Arens product is investigated, where G is any discrete group and \(\mathcal {A}\) is a Banach algebra containing a complemented algebraic copy of \((\ell ^1(\mathbb N),\bullet )\). We give an explicit family of annihilators(w.r.t both the Arens product) in the algebra \(\ell ^1(G,\mathcal
-
On a Slice Hyper-Meromorphic Bergman Space Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-26 Sofia Boudrai, Aiad Elgourari, Allal Ghanmi
We intend to introduce and investigate a new functional space on the quaternionic unit ball of slice hyper-meromorphic functions with unique pole at the origin. Mainly, we provide a concrete characterization of their elements and give the closed explicit expression of the associated reproducing kernel function. Moreover, we show that they are isometrically isomorphic to the configuration space on the
-
Quadratic Fock Space Calculus (II): Positivity of the Preservation Operator and Linear Independence of the Quadratic Exponential Vectors Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-26 Omar Alzeley, Habib Rebei, Hafedh Rguigui
It have been proved in Accardi and Dhahri (J Math Phys 51:2, 2010) that the set of the exponential vectors \(\Phi (g), \; g\in {\mathcal {K}}:=L^2({\mathbb {R}}^d)\cap L^{\infty }({\mathbb {R}}^d)\) associated with different test functions \(g_i\in {\mathcal {K}}\), are linearly independents. Even this result is true, we present an alternative proof that is consistent with the results of this paper
-
Characterization of Dual Scalable Frames Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-25 Behine Heydarpour, Ali Akbar Arefijamaal, Arash Ghaani Farashahi
-
Traces for Sturm–Liouville Operators on a Caterpillar Graph Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-25 Feng Wang, Chuan-Fu Yang, Natalia P. Bondarenko
-
Geometry of Five Point Sets in the Complex Ball Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-24 Richard Rochberg
We describe ten geometric functionals, four real and six complex, which determine the geometry of five point sets in the complex ball up to conformal automorphism. We give conditions on those parameters which are necessary and sufficient for there to be an associated five point set.
-
Several Properties of a Class of Generalized Harmonic Mappings Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-23 Bo-Yong Long, Qi-Han Wang
We call the solution of a kind of second order homogeneous partial differential equation as real kernel \(\alpha \)-harmonic mappings. In this paper, the representation theorem, the Lipschitz continuity, the univalency and the related problems of the real kernel \(\alpha \)-harmonic mappings are explored.
-
Estimation of Bounds for the Zeros of Polynomials and Regular Functions of a Quaternionic Variable Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-23 Abdullah Mir, Abrar Ahmad
The estimation of zeros of a polynomial with quaternionic coefficients has been done by many mathematicians in the recent past using various approaches. In this paper, we estimate the upper bounds for the zeros of polynomials and derive zero-free regions of some special regular functions of a quaternionic variable with restricted coefficients using the extended Schwarz’s lemma and the zero sets of
-
Browder S-Resolvent Equation in Quaternionic Setting Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-22 Hatem Baloudi, Aref Jeribi, Habib Zmouli
This paper is devoted to the study of the S-eigenvalue of finite type of a bounded right quaternionic linear operator acting in a right quaternionic Hilbert space. The study is based on the different properties of the Riesz projection associated with the connected part of the S-spectrum. Furthermore, we introduce the left and right Browder S-resolvent operators. Inspired by the S-resolvent equation
-
Minimal Invariant Subspaces for an Affine Composition Operator Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-18 João R. Carmo, Ben Hur Eidt, S. Waleed Noor
The composition operator \(C_{\phi _a}f=f\circ \phi _a\) on the Hardy–Hilbert space \(H^2({\mathbb {D}})\) with affine symbol \(\phi _a(z)=az+1-a\) and \(0
-
Truncated Second Main Theorem for Holomorphic Curves on Annuli with Moving Hyperplanes Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-15 Nhung Thi Nguyen, An Van Nguyen
In this paper, we establish some truncated second main theorems for holomorphic curve from an annulus into \({\mathbb {P}}^n({\mathbb {C}})\) and moving hyperplanes. We also use these results to solve unique problems with moving targets.
-
Hardy Type Theorems for Linear Canonical Dunkl Transform Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-13 Ahmed Saoudi
In this paper, we establish an analogue of Hardy’s theorems for the linear canonical Dunkl transform and fractional Dunkl transform, which generalizes a large class of a family of integral transforms. As application, we derive Hardy type theorems for fractional Hankel type transform, one dimension Dunkl Fresnel transform, linear canonical transform and fractional Fourier transform.
-
Complex Symmetry of Linear Combinations of Composition Operators on the McCarthy–Bergman Space of Dirichlet Series Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-12 Cheng-shi Huang, Zhi-jie Jiang
-
On the Resolvent Matrix of the Truncated Hausdorff Matrix Moment Problem Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-11
Abstract We obtain the resolvent matrix of the truncated Hausdorff matrix moment (THMM) problem on the interval [a, b] in case of an even and odd number of moments expressed in terms of terminal point b. An explicit relation between the resolvent matrices of the THMM problem with respect to terminal points a and b is presented.
-
Two q-Operational Equations and Hahn Polynomials Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-10
Abstract Motivated by Liu’s (Sci China Math 66:1199–1216, 2023) recent work. This article reveals the essential features of Hahn polynomials by presenting a new q-exponential operator, that is $$\begin{aligned} \exp _q(t\Delta _{x,a})f(x)=\frac{(axt;q)_{\infty }}{(xt;q)_{\infty }} \sum _{n=0}^{\infty }\frac{t^n}{(q;q)_n} f(q^n x) \end{aligned}$$ with \(\Delta _{x,a}=x (1-a)\eta _a+\eta _x\) and \(\eta
-
Approximation by Meromorphic k-Differentials on Compact Riemann Surfaces Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-10 Nadya Askaripour
The main theorem of this article is a Runge type theorem proved for k-differentials \((k\ge 2)\). The integrability in the \(L^1\)- norm is defined for k-differentials in Section 2. We consider k-differentials which are integrable in the defined \(L^1\)- norm on the Riemann surface, and are holomorphic on an open subset of that surface. We will show those k-differentials can be approximated by meromorphic
-
On Decomposition for Pairs of Twisted Contractions Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-10
Abstract This paper presents Wold-type decomposition for various pairs of twisted contractions on Hilbert spaces. We achieve an explicit decomposition for pairs of twisted contractions such that the c.n.u. parts of the contractions are in \(C_{00}\) . The structure for pairs of doubly twisted operators consisting of a power partial isometry has been discussed. It is also shown that for a pair \((T
-
Fredholm Index of 3-Tuple of Restriction Operators and the Pair of Fringe Operators for Submodules in $$H^2({\mathbb {D}}^3)$$ Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-09 Xilin Nie, Anjian Xu
For a submodule \({\mathcal {M}}\) in Hardy module \(H^2({\mathbb {D}}^n)\) on the unit polydisc in \(\mathbb {C}^{n}\), we define the \(n-1\) tuple of fringe operators \(\textbf{F}=(F_{1},F_{2},\ldots ,F_{n-1})\) and the n tuple of restriction operators \(\textbf{R}=(R_{z_{1}},R_{z_{2}},\ldots , R_{z_{n}})\) with respect to \({\mathcal {M}}\). In this paper, for the case \(n=3\), it is shown that
-
Least Energy Sign-Changing Solution for N-Kirchhoff Problems with Logarithmic and Exponential Nonlinearities Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-08 Ting Huang, Yan-Ying Shang
In this paper, we are concerned with the existence of least energy sign-changing solutions for the following N-Laplacian Kirchhoff-type problem with logarithmic and exponential nonlinearities: $$\begin{aligned} \left\{ \begin{array}{ll} -\left( a+b \int _{\Omega }|\nabla u|^{N} d x\right) \Delta _{N} u=|u|^{p-2} u \ln |u|^{2}+\lambda f(u), &{} \text{ in } \Omega , \\ u=0, &{} \text{ on } \partial \Omega
-
Abstract Algebraic Construction in Fractional Calculus: Parametrised Families with Semigroup Properties Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-08 Arran Fernandez
What structure can be placed on the burgeoning field of fractional calculus with assorted kernel functions? This question has been addressed by the introduction of various general kernels, none of which has both a fractional order parameter and a clear inversion relation. Here, we use ideas from abstract algebra to construct families of fractional integral and derivative operators, parametrised by
-
On a Class of Subdiagonal Algebras Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-04
Abstract We investigate some new classes of operator algebras which we call semi- \(\sigma \) -finite subdiagonal and Riesz approximable. These constitute the most general setting to date for a noncommutative Hardy space theory based on Arveson’s subdiagonal algebras. We develop this theory and study the properties of these new classes.
-
On Perturbation of Operators and Rayleigh-Schrödinger Coefficients Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-04 Marcus Carlsson, Olof Rubin
Let A and E be self-adjoint matrices or operators on \(\ell ^2({{\mathbb {N}}})\), where A is fixed and E is a small perturbation. We study how the eigenvalues of \(A+E\) depend on E, with the aim of obtaining second order formulas that are explicitly computable in terms of the spectral decomposition of A and a certain block decomposition of E. In particular we extend the classical Rayleigh-Schrödinger
-
Boas Type Results for Two-Sided Quaternion Fourier Transform and Uniform Lipschitz Spaces Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-04
Abstract For the quaternion algebra \({\mathbb {H}}\) and \(f:\mathbb R^2\rightarrow {\mathbb {H}}\) , we consider a two-sided quaternion Fourier transform \(\widehat{f}\) . Necessary and sufficient conditions for f to belong to generalized uniform Lipschitz spaces are given in terms of behavior of \(\widehat{f}\) .
-
On the Toeplitz Algebra in the Case of All Entire Functions and All Functions Holomorphic in the Unit Disc Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-02 M. Jasiczak
We study the algebra generated by all Toeplitz operators on the Fréchet space of all entire functions and all functions holomorphic in the unit disk. In both cases we prove that the quotient algebra by the commutator ideal can be equipped with a locally convex topology which makes this quotient algebra algebraically and topologically isomorphic with the symbol algebra. We also show that the topology
-
Fractional Integration on Mixed Norm Spaces. I Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-02 Feng Guo, Xiang Fang, Shengzhao Hou, Xiaolin Zhu
In this paper we characterize completely the septuple $$\begin{aligned} (p_1, p_2, q_1, q_2; \alpha _1, \alpha _2; t) \in (0, \infty ]^4 \times (0, \infty )^2 \times {\mathbb {C}} \end{aligned}$$ such that the fractional integration operator \({\mathfrak {I}}_t\), of order \(t \in {\mathbb {C}}\), is bounded between two mixed norm spaces: $$\begin{aligned} {\mathfrak {I}}_t: H(p_1, q_1, \alpha _1)
-
Variational Principles in Quaternionic Analysis with Applications to the Stationary MHD Equations Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-01 P. Cerejeiras, U. Kähler, R. S. Kraußhar
In this paper we aim to combine tools from variational calculus with modern techniques from quaternionic analysis that involve Dirac type operators and related hypercomplex integral operators. The aim is to develop new methods for showing geometry independent explicit global existence and uniqueness criteria as well as new computational methods with special focus to the stationary incompressible viscous
-
Higgs Algebras in Classical Harmonic Analysis Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-01 David Eelbode
In this paper, we will prove that the reproducing kernels \(Z_k({\underline{x}},{\underline{u}})\) for the spaces \({\mathcal {H}}_k({\mathbb {R}}^m,{\mathbb {C}})\) of k-homogeneous harmonics can be seen as elements of an infinite-dimensional ladder operator representation for a cubic polynomial angular momentum algebra which is known as the Higgs algebra. This algebra will be shown to be one of two
-
$$\varepsilon $$ -Numerical Range of Operator Polynomial Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-23 Kamel Mahfoudhi
Relying on some ideas of numerical ranges, we introduce, for operators polynomials on a complex Hilbert space, a new notion called the \(\varepsilon \)-numerical range of operators polynomials. Some geometrical and topological properties of these \(\varepsilon \)-numerical range are proved. Thereby, we achieve a new characterization of \(\varepsilon \)-numerical range of operators polynomials on an
-
Harmonic Bergman Spaces on the Real Hyperbolic Ball: Atomic Decomposition, Interpolation and Inclusion Relations Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-22 A. Ersin Üreyen
For \(\alpha >-1\) and \(0
-
Non-tangential Limits and Bounded Point Derivations on $$R^2(X)$$ Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-21 Stephen Deterding
We study \(L^2\) approximations of rational functions on the complex plane, focusing on bounded point derivations. We show that if there is a bounded point derivation at x and \(\{x_n\}\) is a sequence of points that converges non-tangentially to x, then the sequence of derivatives \(\{f^{\prime }(x_n)\}\) is uniformly bounded for a large class of functions, specifically those functions which can be
-
Hankel Operators Between Different Fock–Sobolev Type Spaces Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-19 Jianjun Chen, Xiaofeng Wang, Jin Xia, Guangxia Xu
In this paper, we study Hankel operators on the Fock–Sobolev type spaces for all possible \(1\le p,q<\infty \) and \(\alpha \in {\mathbb {R}}\). We introduce a function space called integrable mean oscillation on \({\mathbb {C}}^n\). Then we characterize those symbols f for which the Hankel operators \(H^\alpha _f\) and \(H^\alpha _{{{\bar{f}}}}\) are simultaneously bounded (or compact) from Fock–Sobolev
-
Hadamard–Bergman Operators on Weighted Spaces Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-16 Alexey Karapetyants, Adolf Mirotin, Evelin Morales
This article continues the study of the Hadamard–Bergman operators in the unit disc of the complex plane. These operators arose as a natural generalization of the orthogonal projector and represent an integral realization of multiplier operators. Here we consider mainly the further development of the theory of such operators in the context of operators of variable order, that is, with kernels depending
-
Generalized Convolution Operator Associated with the (k, a)-Generalized Fourier Transform on the Real Line and Applications Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-12 Hatem Mejjaoli
-
Steven George Krantz (1951 -) Celebrates his 70th Birthday Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-08 Arni S. R. Srinivasa Rao, Siqi Fu, Gregory Knese, Kaushal Verma, Brett Wick
-
Fredholm and Frame-Preserving Weighted Composition Operators Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-07 Jasbir Singh Manhas, Ruhan Zhao
We characterize Fredholm and frame-preserving weighted composition operators on some general Hilbert spaces of holomorphic functions in bounded domains in \({\mathbb {C}}^n\).
-
A Class of Norm Inequalities for Operator Monotone Functions and Hyponormal Operators Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-06 Katarina Bogdanović
-
Difference of Weighted Composition Operators Over the Ball Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-06 Boo Rim Choe, Koeun Choi, Hyungwoon Koo, Inyoung Park
Recently, Choe et al. obtained characterizations for bounded/compact differences of weighted composition operators acting from a standard weighted Bergman space into another over the unit disk. In this paper we extend those results to the ball setting. By devising a new approach regarding test functions, we improve the characterizations as well as the proofs. Namely, the Reproducing Kernel Thesis is
-
Property $$\mathcal {P}$$ and Compact Perturbations Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-31 Ting Ting Zhou, Li Qi Xiu
Let \(\mathcal {H}\) be a complex separable infinite dimensional Hilbert space. An operator T acting on \(\mathcal {H}\) is said to have property \(\mathcal {P}\), if \(\sigma (T)=\sigma _p(T)\) and \(\sigma (T^*)=\sigma _p(T^*)\). In this paper, we characterize those operators which have an arbitrarily small compact perturbation to satisfy property \(\mathcal {P}\). Also, we study the stability of
-
The Bicomplex Dual Fractional Hankel Transform Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-29 Adam Hammam
We provide a concrete characterization of the Bergman space of bicomplex-valued bc-meromorphic functions with a strong pole at the origin of the bicomplex discus. The explicit expression of its reproducing kernel is given, and its integral representation as the range of the bicomplex version of the generalized second Bargmann transform is also considered. In addition, we construct the bicomplex analog
-
Stability Estimates in Determination of Non-orientable Surface from Its Dirichlet-to-Neumann Map Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-27
Abstract Let (M, g) and \((M',g')\) be non-orientable Riemannian surfaces with fixed boundary \(\Gamma \) and fixed Euler characterictic m, and \(\Lambda \) and \(\Lambda '\) be their Dirichlet-to-Neumann maps, respectively. We prove that the closeness of \(\Lambda '\) to \(\Lambda \) in the operator norm implies the existence of the near-conformal diffeomorphism \(\beta \) between (M, g) and \((M'
-
Normal Holomorphic Mappings in Complex Space Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-24 Peter V. Dovbush, Steven G. Krantz
We study normal holomorphic mappings on complex spaces and complex manifolds. Applications are provided.
-
Free Probability on Banach Algebras Induced by Scaled Hypercomplex Numbers Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-23 Ilwoo Cho
In this paper, we construct certain multiplicative algebraic structure \({{\mathcal {G}}}_{t}\), and the corresponding Banach algebra \({{\mathscr {M}}}_{t}\) generated by \({{\mathscr {G}}}_{t}\) over the complex field \({{\mathbb {C}}}\), where \({{\mathscr {G}}}_{t}\) is induced by the \({{\mathbb {R}}}\)-algebra \({{\mathbb {H}}}_{t}\) of all t-scaled hypercomplex numbers, for \(t\in {{\mathbb
-
Existence of Solutions for a Singular Double Phase Kirchhoff Type Problems Involving the Fractional q(x, .)-Laplacian Operator Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-18 Rym Chammem, Abdeljabbar Ghanmi, Mahfoudh Mechergui
In this paper, we consider a class of fractional Laplacian problems involving fractional \(q_{i}(x)\)-laplacian operators \( (i=1:2)\), and a singular nonlinearity. By using variational methods and monotonicity arguments combined with the theory of the generalized Lebesgue Sobolev spaces, we prove the existence of solutions for such problems. An illustrative example is presented to validate the main
-
Existence of Multiple Solution for a Singular p(x)-Laplacian Problem Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-18 A. Ghanmi, L. Mbarki, Debajyoti Choudhuri
We will study the following singular problem $$\begin{aligned} \left\{ \begin{array}{ll} -div(|\nabla \varphi |^{p(x)-2}\nabla \varphi )+\Psi (x)|\varphi |^{p(x)-2}\varphi = a(x)\varphi ^{-\gamma (x)}+\lambda f(x,\varphi ),\quad \text{ in } \Omega , \\ \\ \varphi =0, \quad \text{ on } \partial \Omega . \end{array} \right. \end{aligned}$$ Here \(\Omega \subset \mathbb {R}^N, (N> 2)\) is a bounded domain
-
Fourier Kernels Associated with the Clifford–Helmholtz System Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-17
Abstract In this paper we present a family of solutions of the Clifford–Helmholtz system, which factors the standard Helmholtz equation. All these solutions can be used as integral kernels of generalized Fourier transforms in hypercomplex analysis. We show that in the Laplace domain they have interesting expressions in terms of terminating hypergeometric functions. This allows us to compute recursion