Wavelet Decomposition for Generalized Haar Spaces

Abstract

This paper is devoted to the numerical information flows and piecewise constant splines connected with them. The spline spaces and their wavelet decompositions are discussed. The approximation relations for such splines turn into the decomposition of the unit. In the case of a uniform grid, the coordinate splines of this type are often called the Haar functions. The numerical flows are associated with irregular spline grids. The spaces of the piecewise constant splines associated with an irregular grid are called spaces of the Haar type. This paper discusses the calibration relations, embedding of the Haar type spaces and their wavelet decompositions. The structure of the decomposition/reconstruction algorithms are done. The cases of the finite and the infinite flows are considered.