Article
Bispectrality for matrix Laguerre-Sobolev polynomials
Author/s | Marcellán Español, Francisco
Zurrián, Ignacio Nahuel |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Publication Date | 2024-09 |
Deposit Date | 2024-06-17 |
Published in |
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Abstract | In this contribution we deal with sequences of polynomials orthogonal with respect to a Sobolev type inner product. A banded symmetric operator is associated with such a sequence of polynomials according to the higher order ... In this contribution we deal with sequences of polynomials orthogonal with respect to a Sobolev type inner product. A banded symmetric operator is associated with such a sequence of polynomials according to the higher order difference equation they satisfy. Taking into account the Darboux transformation of the corresponding matrix we deduce the connection with a sequence of orthogonal polynomials associated with a Christoffel perturbation of the measure involved in the standard part of the Sobolev inner product. A connection with matrix orthogonal polynomials is stated. The Laguerre-Sobolev type case is studied as an illustrative example. Finally, the bispectrality of such matrix orthogonal polynomials is pointed out. |
Funding agencies | European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) Ministerio de Ciencia e Innovación (MICIN). España Agencia Estatal de Investigación. España Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). Argentina |
Project ID. | PID2021-122154NBI00
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Citation | Marcellán Español, F. y Zurrián, I.N. (2024). Bispectrality for matrix Laguerre-Sobolev polynomials. Linear Algebra and its Applications, 697, 131-145. https://doi.org/10.1016/j.laa.2023.09.017. |
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