Distributional Solution and Spectral Shift Function of Heun Differential Equation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913600634880000 |
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| author | Idiong, Ubong Sam |
| author_facet | Idiong, Ubong Sam |
| contents | In this work, the Heun operator is written as an element in the universal enveloping algebra of the Lie algebra $\mathscr{G}=\mathscr{L}(G)$ of the Lie group $G=SL(2,\mathbb{C})$. The Green function and the spectral shift function of the exactly solvable Heun operator from the resulting Lie algebraic equation are obtained via Fourier transform over $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05513 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributional Solution and Spectral Shift Function of Heun Differential Equation Idiong, Ubong Sam Classical Analysis and ODEs 34M46, (Primary) 34B27, 16S30 (Secondary) In this work, the Heun operator is written as an element in the universal enveloping algebra of the Lie algebra $\mathscr{G}=\mathscr{L}(G)$ of the Lie group $G=SL(2,\mathbb{C})$. The Green function and the spectral shift function of the exactly solvable Heun operator from the resulting Lie algebraic equation are obtained via Fourier transform over $G$. |
| title | Distributional Solution and Spectral Shift Function of Heun Differential Equation |
| topic | Classical Analysis and ODEs 34M46, (Primary) 34B27, 16S30 (Secondary) |
| url | https://arxiv.org/abs/2412.05513 |