Negativity-preserving transforms of tuples of symmetric matrices
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866915930505740288 |
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| author | Belton, Alexander Guillot, Dominique Khare, Apoorva Putinar, Mihai |
| author_facet | Belton, Alexander Guillot, Dominique Khare, Apoorva Putinar, Mihai |
| contents | Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obtain the classification of negativity preservers by combining recent advances in matrix analysis with some novel arguments relying on well chosen test matrices, Sidon sets from number theory, and analytic properties of absolutely monotone functions. We continue with the analogous classification in the multi-variable setting, revealing for the first time a striking separation of variables, with absolute monotonicity on one side and only homotheties on the other. We conclude with the complex analogue of this result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18041 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Negativity-preserving transforms of tuples of symmetric matrices Belton, Alexander Guillot, Dominique Khare, Apoorva Putinar, Mihai Classical Analysis and ODEs Functional Analysis 15B48 (primary), 15A18, 26A48, 32A05 (secondary) Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obtain the classification of negativity preservers by combining recent advances in matrix analysis with some novel arguments relying on well chosen test matrices, Sidon sets from number theory, and analytic properties of absolutely monotone functions. We continue with the analogous classification in the multi-variable setting, revealing for the first time a striking separation of variables, with absolute monotonicity on one side and only homotheties on the other. We conclude with the complex analogue of this result. |
| title | Negativity-preserving transforms of tuples of symmetric matrices |
| topic | Classical Analysis and ODEs Functional Analysis 15B48 (primary), 15A18, 26A48, 32A05 (secondary) |
| url | https://arxiv.org/abs/2310.18041 |