Reproducing Kernel Hilbert Spaces of Polyanalytic Functions of Infinite Order

Daniel Alpay; Fabrizio Colombo; Kamal Diki; Irene Sabadini

doi:10.1007/s00020-022-02713-4

Reproducing Kernel Hilbert Spaces of Polyanalytic Functions of Infinite Order

Daniel Alpay
, Fabrizio Colombo
, Kamal Diki
, Irene Sabadini

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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¯⁺^z¯^w 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-zw¯)(1-z¯w) and 11-2Rezw¯. The corresponding backward shift operators are introduced and investigated.

Original language	English
Article number	35
Journal	Integral Equations and Operator Theory
Volume	94
Issue number	4
DOIs	https://doi.org/10.1007/s00020-022-02713-4
State	Published - 1 Dec 2022
Externally published	Yes

Keywords

Backward shift operators
Berezin transform
Polyanalytic Fock space of infinite order
Polyanalytic Hardy space of infinite order
Segal–Bargmann transform

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-022-02713-4

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title = "Reproducing Kernel Hilbert Spaces of Polyanalytic Functions of Infinite Order",

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 ezw¯+z¯w 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-zw¯)(1-z¯w) and 11-2Rezw¯. The corresponding backward shift operators are introduced and investigated.",

keywords = "Backward shift operators, Berezin transform, Polyanalytic Fock space of infinite order, Polyanalytic Hardy space of infinite order, Segal–Bargmann transform",

author = "Daniel Alpay and Fabrizio Colombo and Kamal Diki and Irene Sabadini",

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doi = "10.1007/s00020-022-02713-4",

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TY - JOUR

T1 - Reproducing Kernel Hilbert Spaces of Polyanalytic Functions of Infinite Order

AU - Alpay, Daniel

AU - Colombo, Fabrizio

AU - Diki, Kamal

AU - Sabadini, Irene

PY - 2022/12/1

Y1 - 2022/12/1

N2 - 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 ezw¯+z¯w 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-zw¯)(1-z¯w) and 11-2Rezw¯. The corresponding backward shift operators are introduced and investigated.

AB - 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 ezw¯+z¯w 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-zw¯)(1-z¯w) and 11-2Rezw¯. The corresponding backward shift operators are introduced and investigated.

KW - Backward shift operators

KW - Berezin transform

KW - Polyanalytic Fock space of infinite order

KW - Polyanalytic Hardy space of infinite order

KW - Segal–Bargmann transform

UR - https://www.scopus.com/pages/publications/85139521238

U2 - 10.1007/s00020-022-02713-4

DO - 10.1007/s00020-022-02713-4

M3 - Article

AN - SCOPUS:85139521238

SN - 0378-620X

VL - 94

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 4

M1 - 35

ER -

Reproducing Kernel Hilbert Spaces of Polyanalytic Functions of Infinite Order

Abstract

Keywords

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