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Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems

Published online by Cambridge University Press:  14 November 2011

Bernd Carl
Bernd Carl
Affiliation:
Sektion Mathematik, Universität Jena, DDR-69 Jena
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Synopsis

In this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.

Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.

The statements of this paper are obtained by results recently proved elsewhere by the author.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 90 , Issue 1-2 , 1981 , pp. 63 - 70
Copyright
Copyright © Royal Society of Edinburgh 1981

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