Orthogonal polynomials of discrete variable and boundedness of Dirichlet kernel

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For orthogonal polynomials defined by compact Jacobi matrix with exponential decay of the coefficients, precise properties of orthogonality measure is determined. This allows showing uniform boundedness of partial sums of orthogonal expansions with respect to $L^\infty$ norm, which generalize analogous results obtained for little $q$-Legendre, little $q$-Jacobi and little $q$-Laguerre polynomials, by the authors.

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Functional Analysis, 42C15

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http://salesiana.dossiersoluciones.com/handle/123456789/102255

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0509241
 http://arxiv.org/abs/math/0509241

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arXiv