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Descripción
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| In this paper Geronimus transformations for matrix orthogonal polynomials in the real line are studied. The orthogonality is understood in a broad sense, and is given in terms of a nondegenerate continuous sesquilinear form, which in turn is determined by a quasidefinite matrix of bivariate generalized functions with a well defined support. The discussion of the orthogonality for such a sesquilinear form includes, among others, matrix Hankel cases with linear functionals, general matrix Sobolev orthogonality and discrete orthogonal polynomials with an infinite support. The results are mainly concerned with the derivation of Christoffel type formulas, which allow to express the perturbed matrix biorthogonal polynomials and its norms in terms of the original ones. The basic tool is the Gauss?Borel factorization of the Gram matrix, and particular attention is paid to the non-associative character, in general, of the product of semi-infinite matrices. The Geronimus transformation, in where a right multiplication by the inverse of a matrix polynomial and an addition of adequate masses is performed, is considered. The resolvent matrix and connection formulas are given. Two different methods are developed. A spectral one, based on the spectral properties of the perturbing polynomial, and constructed in terms of the second kind functions.This approach requires the perturbing matrix polynomial to have a nonsingular leading term | |
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Internacional
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JCR del ISI
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Si |
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Título de la revista
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Complex Analysis And Operator Theory |
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ISSN
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1661-8254 |
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Factor de impacto JCR
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0,739 |
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Información de impacto
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Volumen
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DOI
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Número de revista
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Desde la página
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3979 |
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Hasta la página
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4005 |
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Mes
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SIN MES |
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Ranking
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