Embeddings of some weighted function spaces on R^n ; entropy and approximation numbers. A survey of some recent results.

by    D.D. Haroske

Preprint series: 98-14, Analysis

The paper is published: Analele Univ. din Craiova, Seria Matematica - Informatica, XXIV, 1-44, 1997

46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
47B06 Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators

Abstract: In this survey we summarise recent results concerning compact embeddings of some weighted function spaces of type B^s_{p,q} and F^s_{p,q} on R^n. We study the asymptotic behaviour of their entropy and approximation numbers. We give some motivation how to apply results of this type in spectral theory.

This survey provides a unified approach of recent outcomes (which have mostly been published before) and marks some present `state of the art' in this field of research.

Keywords: weighted function spaces, compact embeddings, entropy numbers, approximation numbers

Upload: 1998-10-01

Update: 1999-03-01

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