Inequalities associated with certain operators within the framework of weighted Fock spaces: Inequalities associated with certain operators

Fethi Soltani

doi:10.14244/lajm.v5i1.78

Authors

Fethi Soltani Universite de Tunis El Manar https://orcid.org/0000-0001-7519-0994

DOI:

https://doi.org/10.14244/lajm.v5i1.78

Keywords:

Analytic functions, weighted Fock spaces, extremal functions

Abstract

In this paper we introduce a weighted Fock space $\mathscr{F}_{\beta}$. This space which gives a generalization of some Hilbert spaces of analytic functions on the complex plane $\mathbb{C}$ like, the classical Fock space $\mathscr{F}$, the Dunkl type Fock space $\mathscr{F}_{\nu}$ and the Bessel-Struve type Fock space $\mathbb{F}_{\nu}$, it plays a background to our contribution. Especially, we examine the extremal functions for the difference operator $Df(z):=\frac{1}{z^2}(f(z)-zf'(0)-f(0))$, and we deduce approximate inversion formulas for the operator $D$ on the weighted Fock space $\mathscr{F}_{\beta}$.

Author Biography

Fethi Soltani, Universite de Tunis El Manar

[1] Soltani F. Best approximation formulas for the Dunkl L2-multiplier operators on Rd. Rocky Mountain J. Math. 42(1) (2012) 305-328.
[2] Soltani F. Operators and Tikhonov regularization on the Fock space. Integral Transform. Spec. Funct. 25(4) (2014) 283-294.
[3] Soltani F. Some examples of extremal functions on the Fock space F(C). Proc. Inst. Math. Mech. 42(2) (2016) 265-272.
[4] Soltani F. Uncertainty principles for the Segal-Bargmann transform. J. Math. Res. Appl. 37(5) (2017) 563-576.
[5] Soltani F. Applications on the Bessel-Struve-type Fock space. Commun. Korean Math. Soc. 32(4) (2017) 875-883.
[6] Soltani F, Nenni M. Dierence and primitive operators on the Dunkl-type Fock space F(Cd). J. Math. Sci. 266(6) (2022) 917-932.
[7] Soltani F, Nenni M. Heisenberg uncertainty principles for the Dunkl-type Fock space. Complex Anal. Oper. Theory 17(6) (2023) Article 105 (13 pages).
[8] Soltani F, Saadi H. Uncertainty principles for the Weinstein type Segal-Bargmann space. J. Math. Sci. 271(4) (2023) 468-481.

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