On Generators of the Hardy and the Bergman Spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912090304806912 |
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| author | Andreev, Valentin V. Bekker, Miron B. Cima, Joseph A. |
| author_facet | Andreev, Valentin V. Bekker, Miron B. Cima, Joseph A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_04119 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Generators of the Hardy and the Bergman Spaces Andreev, Valentin V. Bekker, Miron B. Cima, Joseph A. Complex Variables Functional Analysis 46E20, 30H10, 30H20 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. |
| title | On Generators of the Hardy and the Bergman Spaces |
| topic | Complex Variables Functional Analysis 46E20, 30H10, 30H20 |
| url | https://arxiv.org/abs/2304.04119 |