Multi-resolution analysis generated by a seed function

TL;DR

This paper presents a method to generate multi-resolution analyses of L^2(R) using a seed function, leveraging a theoretical equivalence with orthonormal sets of wave-functions in quantum physics.

Contribution

It introduces a procedure to construct MRAs from a given square-integrable seed function based on a proven equivalence with quantum wave-functions.

Findings

Provides a systematic way to generate MRAs from seed functions

Links multi-resolution analysis with quantum wave-function sets

Offers potential applications in signal processing and quantum physics

Abstract

In this paper we use the equivalence result originally proved by the author which relates a multi-resolution analysis (MRA) of $L^2(R)$ and an orthonormal set of single electron wave-functions in the lowest Landau level, to build up a procedure which produces, starting with a certain square-integrable function, a MRA of $L^2(R)$