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...
| Autores: | , , , |
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| 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 |
| 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. |
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