We consider the structure of a two-nested first order spline-wavelet decomposition in the case of distant location of elementary nests. We also present algorithms for decomposition and reconstruction and estimate components of the wavelet flow. Bibliography: 2 titles.To study wavelet decompositions of numerical data flows, it is necessary to develop a flexible tool of spline-wavelet approximations with taking into account the smoothness property and the rate of change of the flows. For this purpose one should use spline approximations of different order, nonuniform girds, and decompositions localized in some parts of the domain, as well as nested decompositions for saving computational resources with taking into account the possibilities of parallel computational systems. These topics were covered in the recent papers [1,2].The goal of this paper is to study the structure of a two-nested spline-wavelet decomposition in the case of distant location of elementary nests. As a result, we obtain algorithms for decomposition / reconstruction and estimate the wavelet flow in the case where the initial flow is a sequence of values of a twice continuously differentiable function on a uniform grid.
We study the interference effect of a two-interval comb structure on a grid. We propose decomposition / reconstruction algorithms and discuss the generation of standing waves. We also obtain estimates for components of the wavelet flow in the case where the original flow is a sequence of the values of a twice continuously differentiable function on a uniform grid. Bibliography: 2 titles.
PreliminariesFor any natural number m we denote J m def = {0, 1, . . . , m} and J m def = {−1, 0, 1, . . . , m}. A system of vectors {a i } i∈J m in R 2 is called a complete chain of vectors (cf., for example, [1]) if det(a j−1 , a j ) = 0 for j ∈ J m . Let N be a natural number. On [a, b], we consider a grid
In the space L 2 of periodic functions, sharp (in the sense of constants) lower estimates for the deviation of the modified Steklov functions of the first and second orders in terms of the modulus of continuity are established. Similar results are also obtained for even continuous periodic functions with nonnegative Fourier coefficients in the space C. Bibliography: 3 titles.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.