Approximation numbers of embeddings of Sobolev spaces

1996 ◽  
Vol 221 (2) ◽  
pp. 177-187
Author(s):  
D. E. Edmunds ◽  
A. A. Ilyin
Keyword(s):  
Sobolev Spaces ◽  
Approximation Numbers

Sobolev Spaces

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Sobolev Spaces ◽  
Embedding Theorems ◽  
Approximation Numbers ◽  
Selection Of

This chapter presents a selection of some of the most important results in the theory of Sobolev spacesn. Special emphasis is placed on embedding theorems and the question as to whether an embedding map is compact or not. Some results concerning the k-set contraction nature of certain embedding maps are given, for both bounded and unbounded space domains: also the approximation numbers of embedding maps are estimated and these estimates used to classify the embeddings.

Approximation numbers of embeddings of Sobolev spaces

1996 ◽  
Vol 221 (1) ◽  
pp. 177-187
Author(s):  
D. E. Edmunds ◽  
A. A. Ilyin
Keyword(s):  
Sobolev Spaces ◽  
Approximation Numbers

scholarly journals Approximation numbers of Sobolev embeddings of radial functions on isotropic manifolds

2007 ◽  
Vol 5 (1) ◽  
pp. 27-48 ◽  
Author(s):  
Leszek Skrzypczak ◽  
Bernadeta Tomasz
Keyword(s):  
Asymptotic Formula ◽  
Sobolev Spaces ◽  
Symmetric Spaces ◽  
Approximation Numbers ◽  
Radial Functions ◽  
Sobolev Embeddings ◽  
Rank One

We regard the compact Sobolev embeddings between Besov and Sobolev spaces of radial functions on noncompact symmetric spaces of rank one. The asymptotic formula for the behaviour of approximation numbers of these embeddings is described.

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