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Orthogonal matrix polynomials satisfying differential equations with recurrence coefficients having non-scalar limits

Opened Access Orthogonal matrix polynomials satisfying differential equations with recurrence coefficients having non-scalar limits

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Autor: Borrego Morell, Jorge
Castro Smirnova, Mirta María
Durán Guardeño, Antonio José
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2012-09
Publicado en: Integral Transforms and Special Functions, 23 (9), 685-700.
Tipo de documento: Artículo
Resumen: We introduce a family of weight matrices W of the form T(t)T ∗(t), T(t) = eAteDt 2 , where A is certain nilpotent matrix and D is a diagonal matrix with negative real entries. The weight matrices W have arbitrary size N × N and depend on N parameters. The orthogonal polynomials with respect to this family of weight matrices satisfy a second order differential equation with differential coefficients that are matrix polynomials F2, F1 and F0 (independent of n) of degrees not bigger than 2, 1 and 0 respectively. For size 2 × 2, we find an explicit expression for a sequence of orthonormal polynomials with respect to W. In particular, we show that one of the recurrence coefficients for this sequence of orthonormal polynomials does not asymptotically behave as a scalar multiple of the identity, as it happens in the examples studied up to now in the literature.
Cita: Borrego Morell, J., Castro Smirnova, M.M. y Durán Guardeño, A.J. (2012). Orthogonal matrix polynomials satisfying differential equations with recurrence coefficients having non-scalar limits. Integral Transforms and Special Functions, 23 (9), 685-700.
Tamaño: 229.3Kb
Formato: PDF

URI: http://hdl.handle.net/11441/43377

DOI: 10.1080/10652469.2011.627510

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