Skip to main content
Log in

Criterion of Weak Invertibility in Weighted \(\boldsymbol{L}^{\boldsymbol{p}}\) Spaces of Entire Fock-Type Functions

  • Published:
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) Aims and scope Submit manuscript

Abstract

The complete description of weakly invertible elements in weighted \(L^{p}\) spaces of entire Fock-type functions is obtained in the paper.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. K. Zhu, Analysis on Fock Spaces (Springer, Boston, 2012). https://doi.org/10.1007/978-1-4419-8801-0

  2. M. M. Dzhrbashyan, ‘‘On the representation of some classes of entire functions,’’ Dokl. Akad. Nauk Arm. SSR 7 (5), 193–197 (1947).

    Google Scholar 

  3. M. M. Dzhrbashyan, ‘‘On the problem of the representation of analytic functions,’’ Soobshch. Inst. Mat. Mekh. Akad. Nauk Arm. SSR, No. 2, 3–48 (1948).

    Google Scholar 

  4. M. M. Dzhrbashyan and A. O. Karapetyan, ‘‘Integral representations and uniqueness theorems for entire functions of several variables,’’ Izv. Akad. Nauk Arm. SSR Mat. 26 (1), 3–19 (1991).

    MathSciNet  MATH  Google Scholar 

  5. N. Lindholm, ‘‘Sampling in weighted \(L^{p}\) spaces of entire functions in \(C^{n}\) and estimates of the Bergman kernel,’’ J. Funct. Anal. 182, 390–426 (2001). https://doi.org/10.1006/jfan.2000.3733

    Article  MathSciNet  MATH  Google Scholar 

  6. V. I. Smirnov and N. A. Lebedev, Functions of a Complex Variable: Constructive Theory (Lliffe, London, 1968).

    MATH  Google Scholar 

  7. N. K. Nikolski, Operators, Functions and Systems: An Easy Reading, Vol. 1: Hardy, Hankel, and Toeplitz (Amer. Math. Soc., Boston, MA, 2002).

  8. V. P. Khavin, ‘‘Methods and structure of commutative harmonic analysis,’’ in Commutative Harmonic Analysis I, Ed. by V. P. Khavin and N. K. Nikol’skij (Springer, Berlin, 1991). https://doi.org/10.1007/978-3-662-02732-5_1

  9. F. A. Shamoyan, ‘‘Weak invertibility in some spaces of analytic functions,’’ Dokl. Akad. Nauk Arm. SSR 74, 157–161 (1982).

    MathSciNet  MATH  Google Scholar 

  10. F. A. Shamoyan, ‘‘Weak invertibility in weight spaces of analytic functions,’’ Izv. Math. 60 (5), 1061–1082 (1996). https://doi.org/10.1070/IM1996v060n05ABEH000091

    Article  MathSciNet  MATH  Google Scholar 

  11. K. Izuchi, ‘‘Cyclic vectors in the Fock space over the complex plane,’’ Proc. Am. Math. Soc. 133, 3627–3630 (2005).

    Article  MathSciNet  Google Scholar 

  12. A. Borichev and H. Hedenmalm, ‘‘Harmonic function of maximal growth: invertibility and cyclicity in Bergman spaces,’’ J. Am. Math. Soc. 10, 761–796 (1997).

    Article  MathSciNet  Google Scholar 

  13. A. Zygmund, Trigonometric Series (Cambridge Univ. Press, Cambridge, 1959).

    MATH  Google Scholar 

  14. A. I. Markushevich, The Theory of Analytic Functions (Nauka, Moscow, 1968).

    Google Scholar 

  15. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic Press, New York, 1965).

    Google Scholar 

  16. M. A. Evgrafov, Asymptotic Estimates and Entire Functions (Nauka, Moscow, 1979).

    MATH  Google Scholar 

  17. Sz. Mandelbrojt, Series de Fourier et Classes Quasi-Analytiques de Fonctions (Gauthier-Villars, Paris, 1935).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to F. A. Shamoyan.

Additional information

Translated by E. Oborin

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shamoyan, F.A. Criterion of Weak Invertibility in Weighted \(\boldsymbol{L}^{\boldsymbol{p}}\) Spaces of Entire Fock-Type Functions. J. Contemp. Mathemat. Anal. 55, 307–319 (2020). https://doi.org/10.3103/S1068362320050052

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068362320050052

Keywords:

Navigation