On orthogonal systems of shifts of scaling function on local fields of positive characteristic

Abstract

We present a new method for constructing an orthogonal step scaling function on local fields of positive characteristic, which generates multiresolution analysis.

Necessary and Sufficient Condition for an Orthogonal Scaling Function on Vilenkin Groups

“…The structure of the paper is the following. In Section 1 we describe the algorithm from the paper [11]. In Section 2 we find a necessary condition for scaling function ϕ using the notion of digraphs, and then we prove that this necessary condition is just a rephrased sufficient one we have in the form of the algorithm, which, in turn, proves that the algorithm is a necessary and sufficient condition.…”

“…In [11] another restriction was omitted. The results of this paper no longer requirê ϕ(χ) to satisfy "|φ(χ)| = 0 or 1".…”

p-adic tight wavelet frames

“…Algorithms and methods based on wavelet analysis have become powerfulltools in image signal compression and analysis. Since in zero-dimensional groups the Fourier transform of a step function is again a step function, an interest arose in wavelets on Vilenkin groups [27,28,29], local fields of positive characteristics [6,7,8,9,10,11,13,14,31,26], field of p-adic number [15,23,22,21,18,17,16], and zerodimensional groups [19,25].…”

How to construct wavelets on local fields of positive characteristic

“…For a step refinable function we can describe an algorithm for constructing masks m (χ). We may obtain them using an algorithm presented in [5]. Recall the notation: (see e.g.…”

“…In the article [13], the concept of N -valid tree was introduced and an algorithm for constructing the mask m (0) and correspondent refinable function ϕ was indicated in the field F (1) . In the articles [14], [5] the mask m (0) and correspondent refinable function ϕ were constructed using graph which is obtained from N -valid tree by adding new arcs. But in this case we cannot define "masks" m …”