multiresolution analysis

Graphs with Contours in Multiresolution Analysis on Vilenkin Groups

Authors: Berdnikov G. S.

The aim of this article is to study the problem of constructing mutiresolution analysis on Vilenkin group. Previous papers by S. F. Lukomskii, Iu. S. Kruss and the author present an algorithm for constructing scaling functions ϕ with compact support, Fourier transform of which also has compact support. The description of such algorithm is tightly connected with directed graphs of special structure, which are constructed with the help of so-called N-valid trees. One of the special properties of these graphs is the absence of directed cycles — contours.

On Accuracy of Estimation of the Number of Steps for the Algorithm for Construction of Scaling Function on Local Fields

Authors: Kruss Y. S.

In this paper we discuss a problem of accuracy of estimation of the number of steps for the algorithm for construction of orthogonal scaling function which generates multiresolution analisys on local fields of positive characteristic. The resulting function is a step function with a compact support. The number of steps in the algorithm is closely related to the support of the Fourier transformation of the scaling function. Thus the estimate for number of steps is not only of computational interest. The upper estimate for this number was already known.

MRA on Local Fields of Positive Characteristic

Authors: Lukomskii S. F., Vodolasov A. M.

We prove that the local field of positive characteristic is a vector space over a finite field.