Entropy numbers and Marcinkiewicz-type discretization

1981 ◽

Vol 90 (1-2) ◽

pp. 63-70 ◽

Cited By ~ 5

Author(s):

Bernd Carl

Keyword(s):

Banach Space ◽

Asymptotic Behaviour ◽

Besov Spaces ◽

Eigenvalue Problems ◽

Function Spaces ◽

Sequence Spaces ◽

Entropy Numbers ◽

Diagonal Operators

SynopsisIn 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.

Download Full-text

More on the duality conjecture for entropy numbers

Comptes Rendus Mathematique ◽

10.1016/s1631-073x(03)00102-x ◽

2003 ◽

Vol 336 (6) ◽

pp. 479-482 ◽

Cited By ~ 1

Author(s):

Shiri Artstein ◽

Vitali D Milman ◽

Stanislaw J Szarek

Keyword(s):

Entropy Numbers

Download Full-text

Correction to: Entropy Numbers of Finite Dimensional Mixed-Norm Balls and Function Space Embeddings with Small Mixed Smoothness

Constructive Approximation ◽

10.1007/s00365-021-09556-z ◽

2021 ◽

Author(s):

Sebastian Mayer ◽

Tino Ullrich

Keyword(s):

Function Space ◽

Mixed Norm ◽

Entropy Numbers ◽

Finite Dimensional ◽

And Function ◽

Mixed Smoothness

Download Full-text

Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators

Georgian Mathematical Journal ◽

10.1515/gmj.2001.323 ◽

2001 ◽

Vol 8 (2) ◽

pp. 323-332

Author(s):

A. Meskhi

Keyword(s):

Asymptotic Behavior ◽

Integral Operators ◽

Integral Transforms ◽

Singular Value ◽

Entropy Numbers ◽

Liouville Type ◽

Singular Value Decompositions

Abstract The asymptotic behavior of the singular and entropy numbers is established for the Erdelyi–Köber and Hadamard integral operators (see, e.g., [Samko, Kilbas and Marichev, Integrals and derivatives. Theoryand Applications, Gordon and Breach Science Publishers, 1993]) acting in weighted L 2 spaces. In some cases singular value decompositions are obtained as well for these integral transforms.

Download Full-text