Reproducing Kernel Hilbert Spaces of Polyanalytic Functions of Infinite Order

Authors

Daniel Alpay, Chapman UniversityFollow
Fabrizio Colombo, Politecnico di MilanoFollow
Kamal Diki, Chapman UniversityFollow
Irene Sabadini, Politecnico di MilanoFollow

Document Type

Article

Publication Date

10-7-2022

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^zw+zw 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 − zw)) and 1 / (1 − 2Re zw) . The corresponding backward shift operators are introduced and investigated.

Comments

This is the initial draft of an article that was later underwent peer review and was accepted for publication in Integral Equations and Operator Theory, volume 94, in 2022. The final publication may differ and is available at Springer via https://doi.org/10.1007/s00020-022-02713-4.

The Creative Commons license below applies only to this version of the article.

A free-to-read copy of the final published article is available here.

Recommended Citation

Alpay, D., Colombo, F., Diki, K. et al. Reproducing Kernel Hilbert Spaces of Polyanalytic Functions of Infinite Order. Integr. Equ. Oper. Theory 94, 35 (2022). https://doi.org/10.1007/s00020-022-02713-4

Copyright

This version: the authors. Final, peer-reviewed version: Springer.

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.