On the summability and convergence of formal solutions of linear $q$-difference-differential equations with constant coefficients
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915063043981312 |
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| author | Ichinobe, Kunio Michalik, Sławomir |
| author_facet | Ichinobe, Kunio Michalik, Sławomir |
| contents | We consider the Cauchy problem for homogeneous linear $q$-difference-differential equations with constant coefficients. We characterise convergent, $k$-summable and multisummable formal power series solutions in terms of analytic continuation properties and growth estimates of the Cauchy data. We also introduce and characterise sequences preserving summability, which make a very useful tool, especially in the context of moment differential equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2301_10331 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the summability and convergence of formal solutions of linear $q$-difference-differential equations with constant coefficients Ichinobe, Kunio Michalik, Sławomir Analysis of PDEs Classical Analysis and ODEs Complex Variables 35C10, 35E15, 39A13, 40G10 We consider the Cauchy problem for homogeneous linear $q$-difference-differential equations with constant coefficients. We characterise convergent, $k$-summable and multisummable formal power series solutions in terms of analytic continuation properties and growth estimates of the Cauchy data. We also introduce and characterise sequences preserving summability, which make a very useful tool, especially in the context of moment differential equations. |
| title | On the summability and convergence of formal solutions of linear $q$-difference-differential equations with constant coefficients |
| topic | Analysis of PDEs Classical Analysis and ODEs Complex Variables 35C10, 35E15, 39A13, 40G10 |
| url | https://arxiv.org/abs/2301.10331 |