Relations between multi-resolution analysis and quantum mechanics

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Abstract

We discuss a procedure to construct multiresolution analyses (MRA) of L2 (R) starting from a given seed function h (s) which should satisfy some conditions. Our method, originally related to the quantum mechanical Hamiltonian of the fractional quantum Hall effect, 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. © 2005 American Institute of Physics.
Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalJournal of Mathematical Physics
Volume46
Publication statusPublished - 2005

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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