Abstract
We provide a complete description of zero sets of some new analytic area Nevanlinna type spaces in the unit disk. Our theorems extend recent sharp results of E. Rodikova to larger analytic function spaces of area Nevanlinna type.
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References
M. M. Dzhrbashyan, “The parametric representation of some general classes of meromorphic functions in the unit circle,” Dokl. Akad. Nauk SSSR 157 (5), 1024–1027 (1964).
R. Nevanlinna, Eindeutige analytische Funktionen (Julius Springer, Berlin, 1836).
F. A. Shamoyan, “M. M. Dzrbasjan’s factorization theorem and characteristic of zeros of functions analytic in a disc with majorant finite growth,” Izv. Akad. Nauk Arm. SSR, Mat. 13, 405–422 (1978).
F. A. Shamoyan, “Parametric representation and description of the root sets of weighted classes of functions holomorphic in the disk,” Siberian Math. J. 40 (6), 1211–1229 (1999).
F. A. Shamoyan and E. N. Shubabko, Introduction to the Theory of Weighted Lp-Classes of Meromorphic Functions (Bryansk State University, Bryansk, 2009).
M. M. Dzhrbashyan, “On the problem of representability of analytic functions,” Proc. Inst. Math. Mech. Akad. Nauk Arm. SSR 2, 3–40 (1948).
E. G. Rodikova, “Factorization representation and the description of zero sets for the class of holomorphic functions in a disk,” Sib. Èlektron. Mat. Izv. 11, 52–63 (2014).
E. G. Rodikova, Factorization, Characterization of Root Sets, and Interpolation Problems in Weighted Spaces of Analytic Functions, Cand. Sci. (Phys.–Math.) Dissertation (Bryansk State University, Bryansk, 2014).
R. Shamoyan and H. Li, “Descriptions of zero sets and parametric representations of certain analytic area Nevanlinna type classes in the unit disk,” Kragujevac J. Math. 34, 73–89 (2010).
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Shamoyan, R.F., Tomashevskaya, E.B. A Note on Some New Sharp Results on the Zeros of New Area Nevanlinna Type Spaces in the Unit Disk. Math Notes 114, 1337–1341 (2023). https://doi.org/10.1134/S0001434623110664
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DOI: https://doi.org/10.1134/S0001434623110664