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.
BAGARELLO F (2005). Relations between multi-resolution analysis and quantum mechanics. JOURNAL OF MATHEMATICAL PHYSICS, 46(5), 1-16 [10.1063/1.1887924].
Relations between multi-resolution analysis and quantum mechanics
BAGARELLO, Fabio
2005-01-01
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.
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