Density of Polynomials in Sub-Bergman Hilbert Spaces

TL;DR

This paper proves that polynomials are dense in sub-Bergman Hilbert spaces, which are analogous to de Branges-Rovnyak spaces in the Bergman space setting, confirming a previously open question.

Contribution

It establishes the density of polynomials in sub-Bergman Hilbert spaces, providing a key theoretical result in the analysis of these spaces.

Findings

Polynomials are dense in sub-Bergman Hilbert spaces.

Answers an open question posed by Zhu.

Enhances understanding of the structure of sub-Bergman spaces.

Abstract

The sub-Bergman Hilbert spaces are analogues of de BrangesRovnyak spaces in the Bergman space setting. We prove that the polynomials are dense in sub-Bergman Hilbert spaces. This answers the question posted by Zhu in the affirmative.