Functional Analysis and Approximation pp 189-202 | Cite as
Projections with Norms Smaller than those of the Ultraspherical and Laguerre Partial Sums
Abstract
Norm estimates from above and below for partial sum operators of ultraspherical and Laguerre expansions on a class of weighted Lebesgue spaces are established, using ultraspherical and Laguerre weights with parameters different from the parameters of the orthogonal expansions. It turns out that a suitable shifting of the parameters leads to a considerable reduction of the rate of growth of the operator norms. In this way projection operators on weighted Lebesgue spaces can be constructed, the norms of which are smaller than those of the corresponding partial sums. Thus first upper estimates for the minimal projections in these spaces are obtained.
Keywords
Lebesgue Constant Orthogonal Expansion Minimal Projection Laguerre Function Weighted Lebesgue SpacePreview
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