On a class of Sobolev scalar products in the polynomials |
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Authors: | Leonel Robert Luis Santiago |
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Institution: | a Department of Mathematics, University of Toronto, 100 St. George Street, Toronto, Canada M5S 3G3;b Facultad de Matemática y Computación, Universidad de La Habana, San Lázaro y L, Vedado, Cuba CP 10400 |
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Abstract: | This paper discusses Sobolev orthogonal polynomials for a class of scalar products that contains the sequentially dominated products introduced by Lagomasino and Pijeira. We prove asymptotics for Markov type functions associated to the Sobolev scalar product and an extension of Widom's Theorem on the location of the zeroes of the orthogonal polynomials. In the case of measures supported in the real line, we obtain results related to the determinacy of the Sobolev moment problem and the completeness of the polynomials in a suitably defined weighted Sobolev space. |
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Keywords: | Sobolev inner product Orthogonal polynomials Asymptotics Location of zeroes Determinacy Completeness Favard's Theorem |
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