Sobolev spaces with respect to measures in curves and zeros of Sobolev orthogonal polynomials

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dc.creatorRodríguez, José M.
dc.creatorSigarreta, José M.
dc.date2008-05-30
dc.date.accessioned2026-07-07T09:41:53Z
dc.date.available2026-07-07T09:41:53Z
dc.descriptionIn this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded multiplication operator, for a large class of weights. To have bounded multiplication operator has important consequences in Approximation Theory: it implies the uniform bound of the zeros of the corresponding Sobolev orthogonal polynomials, and this fact allows to obtain the asymptotic behavior of Sobolev orthogonal polynomials. We also obtain some non-trivial results about these Sobolev spaces with respect to measures; in particular, we prove a main result in the theory: they are Banach spaces.
dc.description24 pages, latex
dc.identifierhttps://arxiv.org/abs/0805.4761
dc.identifierhttp://arxiv.org/abs/0805.4761
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161987
dc.subjectFunctional Analysis
dc.subjectClassical Analysis and ODEs
dc.subject41A10, 46E35, 46G10
dc.titleSobolev spaces with respect to measures in curves and zeros of Sobolev orthogonal polynomials
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