Darboux transformations from the Appell-Lauricella operator
| Autor: | Antonia M. Delgado, Lidia Fernández, Plamen Iliev |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Simplex Integrable system Applied Mathematics 010102 general mathematics Mathematics::Classical Analysis and ODEs FOS: Physical sciences Mathematical Physics (math-ph) Differential operator 01 natural sciences 010101 applied mathematics symbols.namesake Operator (computer programming) Mathematics - Classical Analysis and ODEs symbols Classical Analysis and ODEs (math.CA) FOS: Mathematics Partial derivative Jacobi polynomials Isomorphism 0101 mathematics Commutative property Analysis Mathematical Physics Mathematics |
| DOI: | 10.48550/arxiv.1909.07796 |
| Popis: | We define two isomorphic algebras of differential operators: the first algebra consists of ordinary differential operators and contains the hypergeometric differential operator, while the second one consists of partial differential operators in d variables and contains the Appell-Lauricella partial differential operator. Using this isomorphism, we construct partial differential operators which are Darboux transformations from polynomials of the Appell-Lauricella operator. We show that these operators can be embedded into commutative algebras of partial differential operators, containing d mutually commuting and algebraically independent partial differential operators, which can be considered as quantum completely integrable systems. Moreover, these algebras can be simultaneously diagonalized on the space of polynomials leading to extensions of the Jacobi polynomials orthogonal with respect to the Dirichlet distribution on the simplex. |
| Databáze: | OpenAIRE |
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