A Short Note on Wavelet Frames Based on FMRA on Local Fields

M Younus Bhat,Asghar Rahimi

doi:10.1155/2020/3957064

Abstract

The concept of frame multiresolution analysis (FMRA) on local fields of positive characteristic was given by Shah in his paper, Frame Multiresolution Analysis on Local Fields published by Journal of Operators. The author has studied the concept of minimum-energy wavelet frames on these prime characteristic fields. We continued the studies based on frame multiresolution analysis and minimum-energy wavelet frames on local fields of positive characteristic. In this paper, we introduce the notion of the construction of minimum-energy wavelet frames based on FMRA on local fields of positive characteristic. We provide a constructive algorithm for the existence of the minimum-energy wavelet frame on the local field of positive characteristic. An explicit construction of the frames and bases is given. In the end, we exhibit an example to illustrate our algorithm.

Highlights

Let K be a field and a topological space. en, K is called a local field if both K+ and K∗ are locally compact abelian groups, where K+ and K∗ denote the additive and multiplicative groups of K, respectively
Let K be a local field of positive characteristic p > 0 and P be a prime element of K
In this article, we are concerned with a minimum-energy wavelet frame which is more restrictive than a frame multiresolution analysis (FMRA) tight frame on local fields of positive characteristic

Summary

Introduction

Let K be a field and a topological space. en, K is called a local field if both K+ and K∗ are locally compact abelian groups, where K+ and K∗ denote the additive and multiplicative groups of K, respectively. Let K be a local field of positive characteristic p > 0 and P be a prime element of K. In this article, we are concerned with a minimum-energy wavelet frame which is more restrictive than a FMRA tight frame on local fields of positive characteristic. We recall the definition of minimum-energy wavelet frames on local fields of positive characteristic [3]. We provide a constructive algorithm for the existence of the minimumenergy wavelet frame on the local field of positive characteristic.

Notations and Preliminaries

Main Results

Example