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Commuting ordinary differential operators of arbitrary genus and arbitrary rank with polynomial coefficients
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mokhov, O. I. |
| Copyright Year | 2013 |
| Abstract | In this paper we construct examples of commuting ordinary scalar differential operators with polynomial coefficients that are related to a spectral curve of an arbitrary genus g > 0 and to an arbitrary rank r > 1 of the vector bundle of common eigenfunctions of the commuting operators over the spectral curve. This solves completely the well-known existence problem for commuting operators of arbitrary genus and arbitrary rank with polynomial coefficients. The constructed commuting operators of arbitrary rank r > 1 and arbitrary genus g > 0 are given explicitly, they are generated by the Chebyshev polynomials Tr(x). |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1303.4263v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
