In this paper we introduce reproducing kernel Hilbert spaces of polyanalytic functions of infinite order. First we study in details the counterpart of the Fock space and related results in this framework. In this case the kernel function is given by e(z (w) over bar+(z) over barw) which can be connected to kernels of polyanalytic Fock spaces of finite order. Segal-Bargmann and Berezin type transforms are also considered in this setting. Then, we study the reproducing kernel Hilbert spaces of complex-valued functions with reproducing kernel 1/(1 - z (w) over bar)(1 - (z) over barw) and 1/1 - 2Re z (w) over bar. The corresponding backward shift operators are introduced and investigated.

Reproducing Kernel Hilbert Spaces of Polyanalytic Functions of Infinite Order

Colombo F.;Diki K.;Sabadini I.
2022-01-01

Abstract

In this paper we introduce reproducing kernel Hilbert spaces of polyanalytic functions of infinite order. First we study in details the counterpart of the Fock space and related results in this framework. In this case the kernel function is given by e(z (w) over bar+(z) over barw) which can be connected to kernels of polyanalytic Fock spaces of finite order. Segal-Bargmann and Berezin type transforms are also considered in this setting. Then, we study the reproducing kernel Hilbert spaces of complex-valued functions with reproducing kernel 1/(1 - z (w) over bar)(1 - (z) over barw) and 1/1 - 2Re z (w) over bar. The corresponding backward shift operators are introduced and investigated.
2022
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1256119
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