A Hörmander–Fock space

Authors

Daniel Alpay, Chapman UniversityFollow
Fabrizio Colombo, Politecnico di MilanoFollow
Kamal Diki, Chapman UniversityFollow
Irene Sabadini, Politecnico di MilanoFollow
Daniele C. Struppa, Chapman UniversityFollow

Document Type

Article

Publication Date

5-16-2023

Abstract

In a recent paper we used a basic decomposition property of polyanalytic functions of order 2 in one complex variable to characterize solutions of the classical ∂-problem for given analytic and polyanalytic data. Our approach suggested the study of a special reproducing kernel Hilbert space that we call the Hörmander-Fock space that will be further investigated in this paper. The main properties of this space are encoded in a specific moment sequence denoted by η= (η_n)_n≥0 leading to a special entire function E(z) that is used to express the kernel function of the Hörmander-Fock space. We present also an example of a special function belonging to the class ML introduced recently by Alpay et al. and apply a Bochner-Minlos type theorem to this function, thus motivating further connections with the theory of stochastic processes.

Comments

This is an original manuscript of an article that later underwent peer review and was published by Taylor & Francis in Complex Variables and Elliptic Equations in 2023. The definitive publisher-authenticated version is available at https://doi.org/10.1080/17476933.2023.2209856.

Recommended Citation

Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini & Daniele C. Struppa (2023) A Hörmander–Fock space, Complex Variables and Elliptic Equations, https://doi.org/10.1080/17476933.2023.2209856.

Peer Reviewed

1

Copyright

Taylor & Francis