Nonlinear N-term Approximation by Refinable Functions
نویسنده
چکیده
Several almost optimal results are obtained about N-term nonlinear approximation by dilated integer translates of a refinable function associated with a finite mask and a rather general matrix dilation A ∈ GLn(Z). §
منابع مشابه
Local Linear Independence of Refinable Vectors of Functions
This paper is devoted to a study of local linear independence of refinable vectors of functions. A vector of functions φ = (φ1, . . . , φr) ∈ (C(IR))r is said to be refinable if it satisfies the vector refinement equation φ(x) = ∑ α∈Z s a(α)φ(2x− α), where a is a finitely supported sequence of r×r matrices called the refinement mask. A complete characterization for the local linear independence...
متن کاملThe combined reproducing kernel method and Taylor series for solving nonlinear Volterra-Fredholm integro-differential equations
In this letter, the numerical scheme of nonlinear Volterra-Fredholm integro-differential equations is proposed in a reproducing kernel Hilbert space (RKHS). The method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro...
متن کاملApproximation properties of multivariate wavelets
Wavelets are generated from refinable functions by using multiresolution analysis. In this paper we investigate the approximation properties of multivariate refinable functions. We give a characterization for the approximation order provided by a refinable function in terms of the order of the sum rules satisfied by the refinement mask. We connect the approximation properties of a refinable fun...
متن کاملProjectable Multivariate Refinable Functions and Biorthogonal Wavelets
A biorthogonal wavelet is derived from a pair of biorthogonal refinable functions using the standard technique in multiresolution analysis. In this paper, we introduce the concept of projectable refinable functions and demonstrate that many multivariate refinable functions are projectable; that is, they essentially carry the tensor product (separable) structure though themselves may be non-tens...
متن کاملSome results of 2-periodic functions by Fourier sums in the space Lp(2)
In this paper, using the Steklov function, we introduce the generalized continuity modulus and denethe class of functions Wr;kp;' in the space Lp. For this class, we prove an analog of the estimates in [1]in the space Lp.
متن کامل