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Approximation Numbers of Maps on Besov Sequence Spaces
Author(s) -
Martins J. S.
Publication year - 1989
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-40.1.120
Subject(s) - diagonal , sequence (biology) , mathematics , operator (biology) , type (biology) , eigenvalues and eigenvectors , besov space , distribution (mathematics) , matrix (chemical analysis) , diagonal matrix , pure mathematics , combinatorics , mathematical analysis , functional analysis , interpolation space , physics , geometry , biochemistry , chemistry , genetics , gene , biology , ecology , materials science , repressor , quantum mechanics , transcription factor , composite material
The asymptotic behaviour of the approximation numbers of embeddings of Besov sequence spaces is studied: under various hypotheses on the parameters, we obtain a n ( I : b p , u λ → b q , υ μ )≍ n u−λ+θ , where θ = max{1/ q −1/p, min[0,max(l/ q −1/2,1/2 − 1/ P )]}. We use these results to characterise diagonal operators acting between Besov sequence spaces by their approximation numbers. Finally we study the eigenvalue distribution for the composition of a diagonal operator and a matrix operator of Besov type.