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Wavelet bases and entropy numbers in weighted function spaces

✍ Scribed by Dorothee D. Haroske; Hans Triebel

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
289 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The aim of this paper is twofold. First we prove that inhomogeneous wavelets of Daubechies type are unconditional Schauder bases in weighted function spaces of B^s^~pq~ and F^s^~pq~ type. Secondly we use these results to estimate entropy numbers of compact embeddings between these spaces. (Β© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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The necessary density condition in C known for sampling and interpolation in the L p space of entire functions with a subharmonic weight is extended to the case of a 2-homogeneous, plurisubharmonic weight function in C. The method is by estimating the eigenvalues of a certain Toeplitz concentration