# The Fock space as a de Branges-Rovnyak space

## TL;DR

This paper demonstrates that de Branges-Rovnyak spaces encompass various classical spaces like Hardy, Fock, and Dirichlet spaces, providing a unified framework and new methods for solving interpolation problems in the Fock space.

## Contribution

It introduces a general framework linking de Branges-Rovnyak spaces to multiple classical spaces, enabling unified analysis and interpolation solutions.

## Key findings

- De Branges-Rovnyak spaces include Hardy, Fock, and Dirichlet spaces as special cases.
- A unified construction approach for these spaces is presented.
- New interpolation methods for the Fock space are developed.

## Abstract

We show that de Branges-Rovnyak spaces include as special cases a number of spaces, such as the Hardy space, the Fock space, the Hardy-Sobolev space and the Dirichlet space. We present a general framework in which all these spaces can be obtained by specializing a sequence that appears in the construction. We show how to exploit this approach to solve interpolation problems in the Fock space.