On polynomial solutions of certain finite order ordinary differential equations
Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well as the corresponding eigenvalues. Also, some linear transfor...
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| creator | Anguas, L. M Rolanía, D. Barrios |
| description | Some properties and relations satisfied by the polynomial solutions of a
bispectral problem are studied. Given a finite order differential operator,
under certain restrictions, its polynomial eigenfunctions are explicitly
obtained, as well as the corresponding eigenvalues. Also, some linear
transformations are applied to sequences of eigenfunctions and a necessary
condition for this to be a sequence of eigenfunctions of a new differential
operator is obtained. These results are applied to the particular case of
classical Hermite polynomials. |
| doi_str_mv | 10.48550/arxiv.2309.10059 |
| format | Article |
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bispectral problem are studied. Given a finite order differential operator,
under certain restrictions, its polynomial eigenfunctions are explicitly
obtained, as well as the corresponding eigenvalues. Also, some linear
transformations are applied to sequences of eigenfunctions and a necessary
condition for this to be a sequence of eigenfunctions of a new differential
operator is obtained. These results are applied to the particular case of
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bispectral problem are studied. Given a finite order differential operator,
under certain restrictions, its polynomial eigenfunctions are explicitly
obtained, as well as the corresponding eigenvalues. Also, some linear
transformations are applied to sequences of eigenfunctions and a necessary
condition for this to be a sequence of eigenfunctions of a new differential
operator is obtained. These results are applied to the particular case of
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bispectral problem are studied. Given a finite order differential operator,
under certain restrictions, its polynomial eigenfunctions are explicitly
obtained, as well as the corresponding eigenvalues. Also, some linear
transformations are applied to sequences of eigenfunctions and a necessary
condition for this to be a sequence of eigenfunctions of a new differential
operator is obtained. These results are applied to the particular case of
classical Hermite polynomials.</abstract><doi>10.48550/arxiv.2309.10059</doi><oa>free_for_read</oa></addata></record> |
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| source | arXiv.org |
| subjects | Mathematics - Functional Analysis |
| title | On polynomial solutions of certain finite order ordinary differential equations |
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