The best image-term approximations on generalized Besov classes image with regard to orthogonal dictionaries Original Research Article

In this paper, we investigate nonlinear mm-term approximation with regard to orthogonal dictionaries. We consider this problem in the periodic multivariate case for generalized Besov classes View the MathML sourceMBq,θΩ under the condition View the MathML sourceΩ(t)=ω(t1⋅⋯⋅td) where View the MathML sourceω(t)∈Ψl∗ is a univariate function. We prove that the well-known dictionary UdUd which consists of trigonometric polynomials (shifts of the Dirichlet kernels) is nearly optimal among orthogonal dictionaries. Moreover, it is established that for these classes near-best mm-term approximation, with regard to UdUd, can be achieved by simple greedy-type algorithms.