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

TL;DR

This paper introduces a novel method for constructing orthogonal step scaling functions on local fields of positive characteristic, enabling the development of multiresolution analysis in this mathematical setting.

Contribution

It presents a new approach to construct orthogonal scaling functions on local fields of positive characteristic, expanding multiresolution analysis techniques.

Findings

New method for constructing orthogonal scaling functions

Enables multiresolution analysis on local fields of positive characteristic

Advances mathematical tools for signal processing in non-Archimedean settings

Abstract

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