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

The aim of this paper is threefold. Firstly, we deal with approximation numbers of compact embeddings B-pp(s) (R-n) curved right arrow L-p(mu), s > 0, 1 < p < infinity, where p is an (isotropic) Radon measure in R-n. Secondly, we apply the outcome to study the distribution of the eigenvalues of fractal elliptic operators B-s = (id - Delta)(-s)(degrees)mu, s > 0. Thirdly, we wish to demonstrate that the theory of subatomic wavelet frames in function spaces according to (Studia Math. 154 (2003) 59) is an efficient tool to handle problems of this and related type. (C) 2004 Elsevier Inc. All rights reserved.