p-Adic Scaling Set and Generalized Scaling Set

TL;DR

This paper extends multiresolution analysis and wavelet theory to the p-adic field Qp by developing the concepts of scaling sets and generalized scaling sets, which are crucial for constructing wavelet bases.

Contribution

It introduces the theory of scaling sets and generalized scaling sets specifically for Qp, filling a gap in wavelet theory on local fields of positive characteristic.

Findings

Characterization of generalized scaling sets on Qp

Necessary conditions for scaling sets in Qp

Examples illustrating the theory

Abstract

The main goal of this paper is to develop the MRA theory along with wavelet theory in L2(Qp). Generalized scaling sets are important in wavelet theory because it determine multiwavelet sets. Although the theory of scaling set and generalized scaling set on R and many other local field of positive characteristic are available but not on Qp. This article contains discussion of some necessary conditions of scaling set and characterize generalized scaling set with examples.