De Branges spaces and Fock spaces

TL;DR

This paper explores the relationship between de Branges spaces and Fock spaces, demonstrating that de Branges spaces can be represented as Fock-type spaces with equivalent norms and providing explicit constructions for representing weights.

Contribution

It establishes a connection between de Branges and Fock spaces, offering new constructions of weights and explicit descriptions for special classes.

Findings

Any de Branges space can be realized as a Fock-type space with equivalent area norm.

Constructed several methods for representing weights in these spaces.

Explicitly described de Branges spaces for weights depending on the imaginary part only.

Abstract

Relations between two classes of Hilbert spaces of entire functions, de Branges spaces and Fock-type spaces with non-radial weights, are studied. It is shown that any de Branges space can be realized as a Fock-type space with equivalent area norm, and several constructions of a representing weight are suggested. For some special classes of weights (e.g., weights depending on the imaginary part only) the corresponding de Branges spaces are explicitly described.