Approximation numbers in function spaces and the distribution of eigenvalues of some fractal elliptic operators

Authors:
Hans Triebel
Affiliations:
Mathematisches Institut, Friedrich-Schiller-Universität Jena, D-07740 Jena, Germany
Venue:
Journal of Approximation Theory
Year:
2004

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Abstract

The aim of this paper is threefold. Firstly, we deal with approximation numbers of compact embeddings Bspp(Rn)→Lp(µ), s 0, 1 p n. Secondly, we apply the outcome to study the distribution of the eigenvalues of fractal elliptic operators Bs = (id - Δ)-s ∘ µ, s 0.Thirdly, we wish to demonstrate that the theory of subatomic wavelet flames in function spaces according to (Studia Math. 154 (2003) 59) is an efficient tool to handle problems of this and related type.