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arXiv:2002.09980 [math.CA]AbstractReferencesReviewsResources

Orthogonal Systems of Spline Wavelets as Unconditional Bases in Sobolev Spaces

Rajula Srivastava

Published 2020-02-23Version 1

We exhibit the necessary range for which functions in the Sobolev spaces $L^s_p$ can be represented as an unconditional sum of orthonormal spline wavelet systems, such as the Battle-Lemari\'e wavelets. We also consider the natural extensions to Triebel-Lizorkin spaces. This builds upon, and is a generalization of, previous work of Seeger and Ullrich, where analogous results were established for the Haar wavelet system.

Comments: 21 pages, 1 figure
Categories: math.CA, cs.NA, math.FA, math.NA
Subjects: 46E35, 46B15, 42C40
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