Coherent pairs of moment functionals of the second kind and associated orthogonal polynomials and Sobolev orthogonal polynomials

Given a pair of quasi-definite moment functionals {v0,v1} we introduce the concept of coherence of the second kind in terms of an algebraic relation that the corresponding sequences of orthogonal polynomials satisfy. We characterize such moment functionals and give some illustrative examples taking...

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Detalles Bibliográficos
Autores: Hancco Suni, M. [UNESP], Marcato, G. A. [UNESP], Marcellán, F., Sri Ranga, A. [UNESP]
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/248429
Acceso en línea:http://dx.doi.org/10.1016/j.jmaa.2023.127118
http://hdl.handle.net/11449/248429
Access Level:acceso abierto
Palabra clave:Coherent pairs of the second kind
Jacobi matrices
Moment functionals
Orthogonal polynomials
Semiclassical moment functionals
Sobolev orthogonal polynomials
Descripción
Sumario:Given a pair of quasi-definite moment functionals {v0,v1} we introduce the concept of coherence of the second kind in terms of an algebraic relation that the corresponding sequences of orthogonal polynomials satisfy. We characterize such moment functionals and give some illustrative examples taking into account they are semiclassical of class at most one. The relation between the corresponding monic Jacobi matrices is stated. For a pair of moment functionals satisfying the coherence property of the second kind, a Sobolev inner product is introduced. The connection formulas between the sequence of monic orthogonal polynomials associated with such a Sobolev inner product and the sequence of monic polynomials orthogonal with respect to the moment functional v0 are given.