Wavelets and orthogonal polynomials based on harmonic oscillator eigenstates

Authors
Dai, DQ
Citation
Dq. Dai, Wavelets and orthogonal polynomials based on harmonic oscillator eigenstates, J MATH PHYS, 41(5), 2000, pp. 3086-3103
Citations number
10
Categorie Soggetti
Physics
Journal title
JOURNAL OF MATHEMATICAL PHYSICS
ISSN journal
00222488 → ACNP
Volume
41
Issue
5
Year of publication
2000
Pages
3086 - 3103
Database
ISI
SICI code
0022-2488(200005)41:5<3086:WAOPBO>2.0.ZU;2-Q
Abstract
We present a new method for the construction of wavelets. The main tool is the harmonic oscillator eigenstates. With the help of their properties we a re able to construct wavelets which have explicit expressions and have expo nential decay in both time domain and frequency domain. Moreover we get a n ew family of polynomials which are orthogonal in a weighted squarely integr able function space. (C) 2000 American Institute of Physics. [S0022-2488(00 )00205-X].