Quantitative cyclicity, stability, and geometric analysis in weighted Besov spaces
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908338086739968 |
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| author | Sababe, Saeed Hashemi Baghban, Amir |
| author_facet | Sababe, Saeed Hashemi Baghban, Amir |
| contents | We introduce new quantitative measures for cyclicity in radially weighted Besov spaces, including the Drury-Arveson space, by defining cyclicity indices based on potential theory and capacity. Extensions to non-commutative settings are developed, yielding analogues of cyclicity in free function spaces. We also study the stability of cyclic functions under perturbations of both the functions and the underlying weight, and we establish geometric criteria linking the structure of zero sets on the boundary to the failure or persistence of cyclicity. These results provide novel invariants and conditions that characterize cyclicity and the structure of multiplier invariant subspaces in a variety of function spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantitative cyclicity, stability, and geometric analysis in weighted Besov spaces Sababe, Saeed Hashemi Baghban, Amir Functional Analysis Differential Geometry Primary 30H25, 47B32, Secondary 46E22, 30E20 We introduce new quantitative measures for cyclicity in radially weighted Besov spaces, including the Drury-Arveson space, by defining cyclicity indices based on potential theory and capacity. Extensions to non-commutative settings are developed, yielding analogues of cyclicity in free function spaces. We also study the stability of cyclic functions under perturbations of both the functions and the underlying weight, and we establish geometric criteria linking the structure of zero sets on the boundary to the failure or persistence of cyclicity. These results provide novel invariants and conditions that characterize cyclicity and the structure of multiplier invariant subspaces in a variety of function spaces. |
| title | Quantitative cyclicity, stability, and geometric analysis in weighted Besov spaces |
| topic | Functional Analysis Differential Geometry Primary 30H25, 47B32, Secondary 46E22, 30E20 |
| url | https://arxiv.org/abs/2504.18644 |