Best \(m\)-term approximation and Sobolev-Besov spaces of dominating mixed smoothness -- the case of compact embeddings

DOI10.1007/s00365-012-9161-3zbMath1251.41005OpenAlexW2066525883MaRDI QIDQ443896

Winfried Sickel, Markus Hansen

Publication date: 13 August 2012

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-012-9161-3

zbMATH Keywords

sequence spacescompact embeddingsapproximation spacesapproximation numbersreal interpolationentropy numbersbest \(m\)-term approximationfunction spaces of dominating mixed smoothnessGagliardo-Nirenberg type inequalitiestensor product wavelet systems

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Multidimensional problems (41A63) Interpolation between normed linear spaces (46B70) Rate of convergence, degree of approximation (41A25) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (9)

Learning with tree tensor networks: complexity estimates and model selection ⋮ Bernstein numbers of embeddings of isotropic and dominating mixed Besov spaces ⋮ Sparse approximation of some function classes with respect to multiple Haar system on the unit cube ⋮ Rate-optimal sparse approximation of compact break-of-scale embeddings ⋮ Best \(n\)-term approximation of diagonal operators and application to function spaces with mixed smoothness ⋮ Nonlinear approximations of classes of periodic functions of many variables ⋮ Isotropic and dominating mixed Besov spaces: A comparison ⋮ Gelfand numbers related to structured sparsity and Besov space embeddings with small mixed smoothness ⋮ On the optimal constants in the two-sided Stechkin inequalities

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