On Generators of the Hardy and the Bergman Spaces
Complex Variables
2024-10-30 v2 Functional Analysis
Abstract
A function which is analytic and bounded in the Unit disk is called a generator for the Hardy space or the Bergman space if polynomials in that function are dense in the corresponding space. We characterize generators in terms of sub-spaces which are invariant under multiplication by the generator and also invariant under multiplication by z, and study wandering properties of such sub-spaces. Density of bounded analytic functions in the sub-spaces of the Hardy space which are invariant under multiplication by the generator is also investigated.
Keywords
Cite
@article{arxiv.2304.04119,
title = {On Generators of the Hardy and the Bergman Spaces},
author = {Valentin V. Andreev and Miron B. Bekker and Joseph A. Cima},
journal= {arXiv preprint arXiv:2304.04119},
year = {2024}
}
Comments
12 pages