Clark measures for rational inner functions II: general bidegrees and higher dimensions
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| author | Anderson, John T. Bergqvist, Linus Bickel, Kelly Cima, Joseph A. Sola, Alan A. |
| author_facet | Anderson, John T. Bergqvist, Linus Bickel, Kelly Cima, Joseph A. Sola, Alan A. |
| contents | We study Clark measures associated with general two-variable rational inner functions (RIFs) on the bidisk, including those with singularities, and with general $d$-variable rational inner functions with no singularities. We give precise descriptions of support sets and weights for such Clark measures in terms of level sets and partial derivatives of the associated RIF. In two variables, we characterize when the associated Clark embeddings are unitary, and for generic parameter values, we relate vanishing of two-variable weights with the contact order of the associated RIF at a singularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11248 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Clark measures for rational inner functions II: general bidegrees and higher dimensions Anderson, John T. Bergqvist, Linus Bickel, Kelly Cima, Joseph A. Sola, Alan A. Functional Analysis Complex Variables 28A25, 28A35, 32A08, 47A55 We study Clark measures associated with general two-variable rational inner functions (RIFs) on the bidisk, including those with singularities, and with general $d$-variable rational inner functions with no singularities. We give precise descriptions of support sets and weights for such Clark measures in terms of level sets and partial derivatives of the associated RIF. In two variables, we characterize when the associated Clark embeddings are unitary, and for generic parameter values, we relate vanishing of two-variable weights with the contact order of the associated RIF at a singularity. |
| title | Clark measures for rational inner functions II: general bidegrees and higher dimensions |
| topic | Functional Analysis Complex Variables 28A25, 28A35, 32A08, 47A55 |
| url | https://arxiv.org/abs/2303.11248 |