We discuss a procedure to construct multiresolution analyses (MRA) of starting from a given seed function 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.
REFERENCES
1.
J. P.
Antoine
and F.
Bagarello
, J. Phys. A
27
, 2471
(1994
).2.
F.
Bagarello
, J. Phys. A
27
, 5583
(1994
).3.
F.
Bagarello
, J. Phys. A
29
, 565
(1996
).4.
F.
Bagarello
, J. Math. Phys.
42
, 5116
(2001
).5.
F.
Bagarello
, J. Phys. A
36
, 123
(2003
).6.
J. P.
Antoine
and F.
Bagarello
, “Localization properties and wavelet-like orthonormal bases for the lowest Landau level
, in Advances in Gabor Analysis
, edited by H. G.
Feichtinger
and T.
Strohmer
(Birkhäuser
, Boston, 2003
).7.
F.
Bagarello
, J. Math. Phys.
44
, 1519
(2003
).8.
9.
F.
Bagarello
, G.
Morchio
, and F.
Strocchi
, Phys. Rev. B
48
, 5306
(1993
).10.
M.
Moshinsky
and C.
Quesne
, J. Math. Phys.
12
, 1772
(1971
).11.
12.
I.
Dana
and J.
Zak
, Phys. Rev. B
28
, 811
(1983
).13.
I.
Daubechies
, Ten Lectures on Wavelets
(Society for Industrial and Applied Mathematics
, Philadelphia, 1992
).14.
F.
Bagarello
(to be published).15.
S. T.
Ali
and F.
Bagarello
, J. Math. Phys.
(in press).© 2005 American Institute of Physics.
2005
American Institute of Physics
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