A new commutativity property of exceptional orthogonal polynomials
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913400327503872 |
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| author | Castro, M. M. Grünbaum, F. A. |
| author_facet | Castro, M. M. Grünbaum, F. A. |
| contents | We exhibit three examples showing that the "time-and-band limiting" commutative property found and exploited by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960's, and independently by M. Mehta and later by C. Tracy and H. Widom in Random matrix theory, holds for exceptional orthogonal polynomials. The property in question is the existence of local operators with simple spectrum that commute with naturally appearing global ones. We illustrate numerically the advantage of having such a local operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13928 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A new commutativity property of exceptional orthogonal polynomials Castro, M. M. Grünbaum, F. A. Classical Analysis and ODEs Mathematical Physics 33C45, 33C47, 33E30, 42C05 We exhibit three examples showing that the "time-and-band limiting" commutative property found and exploited by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960's, and independently by M. Mehta and later by C. Tracy and H. Widom in Random matrix theory, holds for exceptional orthogonal polynomials. The property in question is the existence of local operators with simple spectrum that commute with naturally appearing global ones. We illustrate numerically the advantage of having such a local operator. |
| title | A new commutativity property of exceptional orthogonal polynomials |
| topic | Classical Analysis and ODEs Mathematical Physics 33C45, 33C47, 33E30, 42C05 |
| url | https://arxiv.org/abs/2210.13928 |