Skip to main content
SpringerLink
Log in

On a sufficient condition for the existence of unconditional bases of reproducing kernels in Fock type spaces with nonradial weights

  • Published:
Analysis and Mathematical Physics Aims and scope Submit manuscript

Abstract

We describe some Fock type spaces which possess unconditional bases of reproducing kernels, the spaces \(\mathcal F_{\varphi }\) of entire functions f such that \(fe^{-\varphi }\in L_2({\mathbb {C}})\), where \(\varphi \) is a subharmonic function, which may be nonradial.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Data availability

The manuscript has no associated data.

References

  1. Seip, K.: Density theorems for sampling and interpolation in the Bargmann-Fock space I. Reine Angew. Math. 429, 91–106 (1992). https://doi.org/10.1515/crll.1992.429.91

    Article  MathSciNet  MATH  Google Scholar 

  2. Seip K., Wallsten R.: Density theorems for sampling and interpolation in the Bargmann-Fock space II. Reine Angew. Math., 429, 107–113 (1992). http://eudml.org/doc/153434

  3. Borichev, A., Dhuez, R., Kellay, K.: Sampling and interpolation in large Bergman and Fock spaces. J. Funct. Anal. 242(2), 563–606 (2007). https://doi.org/10.1016/j.jfa.2006.09.002

    Article  MathSciNet  MATH  Google Scholar 

  4. Borichev, A., Lyubarskii, Yu.: Riesz bases of reproducing kernels in Fock type spaces. J. Inst. Math. Jussieu 9, 449–461 (2010). https://doi.org/10.1017/S147474800900019X

    Article  MathSciNet  MATH  Google Scholar 

  5. Baranov, A., Belov, Yu., Borichev, A.: Fock type spaces with Riesz bases of reproducing kernels and de Branges spaces. Stud. Math. 236(2), 127–142 (2017). https://doi.org/10.4064/sm8504-9-2016

    Article  MathSciNet  MATH  Google Scholar 

  6. Isaev, K.P., Yulmukhametov, R.S.: Unconditional bases in radial Hilbert spaces. Izvestiya Math. 86(1), 150–168 (2022). https://doi.org/10.1070/IM9071

    Article  MathSciNet  MATH  Google Scholar 

  7. Isaev, K.P., Yulmukhametov, R.S.: On a sufficient condition for the existence of unconditional bases of reproducing kernels in Hilbert spaces of entire functions. Lobachevskii J. Math. 42(6), 1154–1165 (2021). https://doi.org/10.1134/S1995080221060093

    Article  MathSciNet  MATH  Google Scholar 

  8. Isaev K.P., Yulmukhametov R.S.: Equivalent conditions for the existence of unconditional bases of reproducing kernels in spaces of entire functions. Problemy Analiza Issues Anal., 10(28)(3), 41–52 (2021). https://doi.org/10.15393/j3.art.2021.10910

  9. Isaev, K.P., Lutsenko, A.V., Yulmukhametov, R.S.: Necessary condition for the existence of unconditional bases of reproducing kernels for Hilbert spaces of entire functions. J. Math. Sci. 257(5), 662–672 (2021). https://doi.org/10.1007/s10958-021-05508-x

    Article  MathSciNet  MATH  Google Scholar 

  10. Isaev, K.P., Yulmukhametov, R.S.: Riesz bases of normalized reproducing kernels in Fock type spaces. Anal. Math. Phys. 12(1), 11 (2022). https://doi.org/10.1007/s13324-021-00623-z

    Article  MathSciNet  MATH  Google Scholar 

  11. Isaev, K.P., Yulmukhametov, R.S.: On a criterion for the existence of unconditional bases of reproducing kernels in Fock spaces with radial regular weight. J. Math. Anal. Appl. 519(2), 126839 (2023). https://doi.org/10.1016/j.jmaa.2022.126839

    Article  MathSciNet  MATH  Google Scholar 

  12. Hayman W. K. and Kennedy P. B.: Subharmonic functions. Vol. 1. London Mathematical Society Monographs No 9, Academic Press, London (1976)

  13. Isaev, K.P., Trunov, K.V., Yulmukhametov, R.S.: Equivalent norms in Hilbert spaces with unconditional bases of reproducing Kernels. J. Math. Sci. 250(2), 310–321 (2020). https://doi.org/10.1007/s10958-020-05017-3

    Article  MathSciNet  MATH  Google Scholar 

  14. Isaev, K.P., Lutsenko, A.V., Yulmukhametov, R.S.: Unconditional bases in weakly weighted spaces of entire functions. St. Petersburg Math. J. 30(2), 253–265 (2019). https://doi.org/10.1090/spmj/1541

    Article  MathSciNet  MATH  Google Scholar 

  15. Isaev, K.P., Lutsenko, A.V., Yulmukhametov, R.S.: Unconditional bases of reproducing kernels for Fock spaces with nonradial weights. J. Math. Sci. 260(6), 748–756 (2022). https://doi.org/10.1007/s10958-022-05725-y

    Article  MathSciNet  MATH  Google Scholar 

  16. Landkof, N.S.: Foundation of Modern Potential Theory. Springer, Berlin (1972)

    Book  MATH  Google Scholar 

Download references

Funding

The research of first and second authors was supported by the grant of Russian Science Foundation (project no. 21-11-00168). The research of third author is made in the framework of executing the Developing Program of Scientific and Educational mathematical center of Privolzhsky Federal District (agreement no. 075-02-2022-888).

Author information

Authors and Affiliations

  1. Ufa University of Science and Technology, 32, Zaki Validi str., Ufa, Russia, 450076

    K. P. Isaev, A. V. Lutsenko & R. S. Yulmukhametov

  2. Ufa Federal Research Centre, Institute of Mathematics, Russian Academy of Sciences (Institute of Mathematics UFRC RAS), 112, Chernyshevsky str., Ufa, Russia, 450008

    K. P. Isaev, A. V. Lutsenko & R. S. Yulmukhametov

Authors
  1. K. P. Isaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Lutsenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. S. Yulmukhametov
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All declared authors wrote the main manuscript text. All authors reviewed the manuscript.

Corresponding author

Correspondence to K. P. Isaev.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

Does not apply.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Isaev, K.P., Lutsenko, A.V. & Yulmukhametov, R.S. On a sufficient condition for the existence of unconditional bases of reproducing kernels in Fock type spaces with nonradial weights. Anal.Math.Phys. 13, 83 (2023). https://doi.org/10.1007/s13324-023-00848-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13324-023-00848-0

Keywords

Mathematics Subject Classification

Search

Navigation