Bispectrality and the ad conditions
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911682895282176 |
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| author | Grunbaum, F. Alberto |
| author_facet | Grunbaum, F. Alberto |
| contents | At the beginning of the study of the bispectral problem, see [18], the ad-conditions played a crucial role in finding non-classical instances. The connection with the ad-conditions has reappeared in several different incarnations of the bispectral problem. Here we show that, properly adapted versions of these conditions, see [44], can play an important role in areas including, for instance, the study of exceptional orthogonal polynomials. This is also true in the non-commutative case. Even at this more advanced stage of the field one may hope that finding explicit solutions of these ad-conditions will provide an additional route to new examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00939 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bispectrality and the ad conditions Grunbaum, F. Alberto Mathematical Physics At the beginning of the study of the bispectral problem, see [18], the ad-conditions played a crucial role in finding non-classical instances. The connection with the ad-conditions has reappeared in several different incarnations of the bispectral problem. Here we show that, properly adapted versions of these conditions, see [44], can play an important role in areas including, for instance, the study of exceptional orthogonal polynomials. This is also true in the non-commutative case. Even at this more advanced stage of the field one may hope that finding explicit solutions of these ad-conditions will provide an additional route to new examples. |
| title | Bispectrality and the ad conditions |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2603.00939 |