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Boundedness properties for Sobolev inner products

Opened Access Boundedness properties for Sobolev inner products

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Autor: Castro Smirnova, Mirta María
Durán Guardeño, Antonio José
Departamento: Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2003-05
Publicado en: Journal of Approximation Theory, 122 (1), 97-111.
Tipo de documento: Artículo
Resumen: Sobolev orthogonal polynomials with respect to measures supported on subsets of the complex plane are considered. The connection between the following properties is studied: the multiplication operator Mp(z) = zp(z) defined on the space P of algebraic polynomials with complex coefficients is bounded with respect to the norm defined by the Sobolev inner product, the supports of the measures are compact and the zeros of the orthogonal polynomials lie in a compact subset of the complex plane. As the main result we prove that the boundedness of the multiplication operator M always implies the compactness of the supports.
Cita: Castro Smirnova, M.M. y Durán Guardeño, A.J. (2003). Boundedness properties for Sobolev inner products. Journal of Approximation Theory, 122 (1), 97-111.
Tamaño: 193.1Kb
Formato: PDF

URI: http://hdl.handle.net/11441/47956

DOI: 10.1016/S0021-9045(03)00037-6

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