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- W3100204813 abstract "We construct a large family of commutative algebras of partial differential operators invariant under rotations. These algebras are isomorphic extensions of the algebras of ordinary differential operators introduced by Grünbaum and Yakimov corresponding to Darboux transformations at one end of the spectrum of the recurrence operator for the Jacobi polynomials. The construction is based on a new proof of their results which leads to a more detailed description of the one-dimensional theory. In particular, our approach establishes a conjecture by Haine concerning the explicit characterization of the Krall–Jacobi algebras of ordinary differential operators. On construit une grande famille des algèbres commutatives dʼopérateurs différentiels invariants par rotation. Ces algèbres sont des extensions isomorphes des algèbres dʼopérateurs différentiels ordinaires introduites par Grünbaum et Yakimov correspondant aux transformations de Darboux dʼun côté du spectre de lʼopérateur de récurrence des polynômes de Jacobi. La construction utilise une nouvelle démonstration de leurs résultats qui conduit à une description plus détaillée de la théorie en dimension un. En particulier, notre approche établit une conjecture de Haine concernant la caractérisation explicite des algèbres de Krall–Jacobi des opérateurs différentiels ordinaires." @default.
- W3100204813 created "2020-11-23" @default.
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- W3100204813 date "2011-11-01" @default.
- W3100204813 modified "2023-10-17" @default.
- W3100204813 title "Krall–Jacobi commutative algebras of partial differential operators" @default.
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- W3100204813 doi "https://doi.org/10.1016/j.matpur.2011.03.001" @default.
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