2008/05/30 by José M. Rodríguez, José M. Rodrı́guez, José M. Sigarreta +2
Mathematics · #41A10 #46E35 #46G10 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Mathematical functions and polynomials #math.CA #math.FA #msc:41A10 #msc:46E35 #msc:46G10
paper · pdf · doi:10.48550/arxiv.0805.4761
24 pages, latex
arxiv created 2008/05/30 · openalex publication_date 2008/05/30 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/01
In 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.