p-adic tight wavelet frames

TL;DR

This paper introduces a straightforward method for constructing tight wavelet frames on p-adic numbers using Pontryagin's duality, avoiding traditional unitary extension techniques.

Contribution

It presents a novel approach to building tight wavelet frames on p-adic fields through step masks and wavelet functions based on duality principles.

Findings

Constructed step wavelet frames on p-adic numbers.

Avoided the use of unitary extension principle.

Utilized Pontryagin's duality for frame construction.

Abstract

We propose a simple method to construct step mask and corresponding step wavelet functions that generate tight wavelet frames on the field of p-adic numbers. To construct tight wavelet frames we do not use the principle of unitary extension, we use Pontryagin's principle of duality.