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Orthogonal matrix polynomials and higher-order recurrence relations

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Autor: Durán Guardeño, Antonio José
Van Assche, Walter
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 1995-04-01
Publicado en: Linear Algebra and its Applications, 219 (1), 261-280.
Tipo de documento: Artículo
Resumen: It is well-known that orthogonal polynomials on the real line satisfy a three-term recurrence relation and conversely every system of polynomials satisfying a three-term recurrence relation is orthogonal with respect to some positive Borel measure on the real line. In this paper we extend this result and show that every system of polynomials satisfying some (2N + 1)-term recurrence relation can be expressed in terms of orthonormal matrix polynomials for which the coefficients are N × N matrices. We apply this result to polynomials orthogonal with respect to a discrete Sobolev inner product and other inner products in the linear space of polynomials. As an application we give a short proof of Krein’s characterization of orthogonal polynomials with a spectrum having a finite number of accumulation points.
Cita: Durán Guardeño, A.J. y Van Assche, W. (1995). Orthogonal matrix polynomials and higher-order recurrence relations. Linear Algebra and its Applications, 219 (1), 261-280.
Tamaño: 179.8Kb
Formato: PDF

URI: http://hdl.handle.net/11441/43389

DOI: 10.1016/0024-3795(93)00218-O

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