Nonlinear wavelet approximation of periodic function classes with generalized mixed smoothness. (English) Zbl 1399.41053
Summary: We study the approximation properties of \(L_q\)-greedy algorithms with respect to the known wavelet type system \(U^d\), which consists of shifts of the Dirichlet kernels on Nikol’skii-Besov and Lizorkin-Triebel function classes with given majorant of a mixed modulus of smoothness.
MSC:
| 41A46 | Approximation by arbitrary nonlinear expressions; widths and entropy |
| 41A63 | Multidimensional problems |
| 42A10 | Trigonometric approximation |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
Keywords:
unconditional basis; best \(m\)-term approximation; greedy algorithm; generalized mixed smoothness; wavelet-type system; trigonometric polynomial; majorantReferences:
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