# The Young type theorem in weighted Fock spaces

## TL;DR

This paper generalizes a theorem about the completeness of biorthogonal systems in weighted Fock spaces, extending classical results from Paley-Wiener and Bargmann-Fock spaces under mild regularity conditions.

## Contribution

It proves that in any radial weighted Fock space, the biorthogonal system to a complete, minimal set of kernels is also complete, broadening the scope of Young's theorem.

## Key findings

- Biorthogonal systems are complete in weighted Fock spaces.
- Generalization of Young's theorem to a broader class of spaces.
- Extension of classical results to weighted Fock space settings.

## Abstract

We prove that for every radial weighted Fock space, the system biorthogonal to a complete and minimal system of reproducing kernels is also complete under very mild regularity assumptions on the weight. This result generalizes a theorem by Young on reproducing kernels in the Paley--Wiener space and a recent result of Belov for the classical Bargmann--Segal--Fock space.