Linear finite difference operators preserving Laguerre-Pólya class
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arXiv
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| Format: | Preprint |
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2016
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| _version_ | 1866912454521389056 |
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| author | Katkova, O. Tyaglov, M. Vishnyakova, A. |
| author_facet | Katkova, O. Tyaglov, M. Vishnyakova, A. |
| contents | We completely describe all finite difference operators of the form $$ Δ_{M_1, M_2, h}(f)(z)=M_1(z) f(z+h) + M_2(z) f(z-h) $$ preserving the Laguerre-Pólya class of entire functions. Here $M_1$ and $M_2$ are some complex functions and $h$ is a nonzero complex number. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1608_03924 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Linear finite difference operators preserving Laguerre-Pólya class Katkova, O. Tyaglov, M. Vishnyakova, A. Classical Analysis and ODEs 30C15, 30D15, 30D35, 26C10 We completely describe all finite difference operators of the form $$ Δ_{M_1, M_2, h}(f)(z)=M_1(z) f(z+h) + M_2(z) f(z-h) $$ preserving the Laguerre-Pólya class of entire functions. Here $M_1$ and $M_2$ are some complex functions and $h$ is a nonzero complex number. |
| title | Linear finite difference operators preserving Laguerre-Pólya class |
| topic | Classical Analysis and ODEs 30C15, 30D15, 30D35, 26C10 |
| url | https://arxiv.org/abs/1608.03924 |