Relations between multi-resolution analysis and quantum mechanics

Abstract

We discuss a procedure to construct multi-resolution analyses (MRA) of $\Lc^2(\R)$ starting from a given {\em seed} function $h(s)$ which should satisfy some conditions. Our method, originally related to the quantum mechanical hamiltonian of the fractional quantum Hall effect (FQHE), is shown to be model independent. The role of a canonical map between certain canonically conjugate operators is discussed. This clarifies our previous procedure and makes much easier most of the original formulas, producing a convenient framework to produce examples of MRA.

References in corpus (2)

• Multi-Resolution Analysis and Fractional Quantum Hall Effect: More Results
• Multi-resolution analysis generated by a seed function

Cited by in corpus (1)

• Gabor-like systems in $L^2({\mathbf{R}}^d)$ and extensions to wavelets