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arXiv · 2603.00939

Bispectrality and the ad conditions

F. Alberto Grunbaum
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Abstract

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.

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F. Alberto Grunbaum. 2026-03-01. Bispectrality and the ad conditions. https://arxiv.org/abs/2603.00939

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