Best \(m\)-term approximation and Lizorkin-Triebel spaces

DOI10.1016/j.jat.2011.02.006zbMath1229.41028OpenAlexW2364128533MaRDI QIDQ2275487

Markus Hansen, Winfried Sickel

Publication date: 9 August 2011

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2011.02.006

zbMATH Keywords

waveletsBesov spacesapproximation spacesreal interpolationLizorkin-Triebel spacesbest \(m\)-term approximationdecay of wavelet coefficients

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Best approximation, Chebyshev systems (41A50)

Related Items

Almost diagonal matrices and Besov-type spaces based on wavelet expansions ⋮ Rate-optimal sparse approximation of compact break-of-scale embeddings ⋮ Besov regularity for operator equations on patchwise smooth manifolds ⋮ Besov regularity of solutions to the \(p\)-Poisson equation ⋮ Best \(m\)-term approximation and Sobolev-Besov spaces of dominating mixed smoothness -- the case of compact embeddings ⋮ Tempered homogeneous function spaces. III ⋮ Besov regularity of solutions to the \(p\)-Poisson equation in the vicinity of a vertex of a polygonal domain ⋮ Spaces of Besov-Sobolev type and a problem on nonlinear approximation ⋮ Nonlinear approximation rates and Besov regularity for elliptic PDEs on polyhedral domains ⋮ Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations

Cites Work

• A discrete transform and decompositions of distribution spaces
• The extension problem for certain function spaces involving fractional orders of differentiability
• A new proof of the Jawerth--Franke embedding
• Function spaces and wavelets on domains
• Approximation spaces
• On spaces of Triebel-Lizorkin type
• Hölder inequalities and sharp embeddings in function spaces of \(B_{pq}^ s\) and \(F_{pq}^ s\) type
• Nonlinear methods of approximation
• Best basis selection for approximation in \(L_p\)
• The thresholding greedy algorithm, greedy bases, and duality
• Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces
• On the degree of nonlinear spline approximation in Besov-Sobolev spaces
• Entropy, universal coding, approximation, and bases properties
• Wavelet compression and nonlinear \(n\)-widths
• Restricted nonlinear approximation
• Optimal approximation of elliptic problems by linear and nonlinear mappings. II
• On a class of interpolation spaces
• Interpolation of normed Abelian groups
• New bases for Triebel-Lizorkin and Besov spaces
• Maximal functions measuring smoothness
• Entropy Numbers and Approximation Numbers in Function Spacess
• Entropy Numbers and Approximation Numbers in Function Spaces, II
• Compression of Wavelet Decompositions
• Some observations on Besov and Lizorkin-Triebel spaces.
• On the Spaces of T<scp>riebel‐</scp>L<scp>izorkin</scp> Type: Pointwise Multipliers and Spaces on Domains
• Greedy algorithms and best \(m\)-term approximation with respect to biorthogonal systems
• Non-linear approximation and interpolation spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item