Abstract
The complete description of weakly invertible elements in weighted \(L^{p}\) spaces of entire Fock-type functions is obtained in the paper.
Similar content being viewed by others
REFERENCES
K. Zhu, Analysis on Fock Spaces (Springer, Boston, 2012). https://doi.org/10.1007/978-1-4419-8801-0
M. M. Dzhrbashyan, ‘‘On the representation of some classes of entire functions,’’ Dokl. Akad. Nauk Arm. SSR 7 (5), 193–197 (1947).
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).
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).
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
V. I. Smirnov and N. A. Lebedev, Functions of a Complex Variable: Constructive Theory (Lliffe, London, 1968).
N. K. Nikolski, Operators, Functions and Systems: An Easy Reading, Vol. 1: Hardy, Hankel, and Toeplitz (Amer. Math. Soc., Boston, MA, 2002).
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
F. A. Shamoyan, ‘‘Weak invertibility in some spaces of analytic functions,’’ Dokl. Akad. Nauk Arm. SSR 74, 157–161 (1982).
F. A. Shamoyan, ‘‘Weak invertibility in weight spaces of analytic functions,’’ Izv. Math. 60 (5), 1061–1082 (1996). https://doi.org/10.1070/IM1996v060n05ABEH000091
K. Izuchi, ‘‘Cyclic vectors in the Fock space over the complex plane,’’ Proc. Am. Math. Soc. 133, 3627–3630 (2005).
A. Borichev and H. Hedenmalm, ‘‘Harmonic function of maximal growth: invertibility and cyclicity in Bergman spaces,’’ J. Am. Math. Soc. 10, 761–796 (1997).
A. Zygmund, Trigonometric Series (Cambridge Univ. Press, Cambridge, 1959).
A. I. Markushevich, The Theory of Analytic Functions (Nauka, Moscow, 1968).
I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic Press, New York, 1965).
M. A. Evgrafov, Asymptotic Estimates and Entire Functions (Nauka, Moscow, 1979).
Sz. Mandelbrojt, Series de Fourier et Classes Quasi-Analytiques de Fonctions (Gauthier-Villars, Paris, 1935).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by E. Oborin
About this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1068362320050052