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arXiv · 2304.04119

On Generators of the Hardy and the Bergman Spaces

Valentin V. Andreev·Miron B. Bekker·Joseph A. Cima
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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.

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Valentin V. Andreev, Miron B. Bekker, Joseph A. Cima. 2023-04-08. On Generators of the Hardy and the Bergman Spaces. https://arxiv.org/abs/2304.04119

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