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Traces of localisation operators with two admissible wavelets

Published online by Cambridge University Press:  17 February 2009

M. W. Wong  and
Zhaohui Zhang
M. W. Wong
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada; e-mail: [email protected].
Zhaohui Zhang
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada; e-mail: [email protected].
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Abstract

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The resolution of the identity formula for a localisation operator with two admissible wavelets on a separable and complex Hilbert space is given and the traces of these operators are computed.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 1 , July 2003 , pp. 17 - 25
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Daubechies, I., “Time-frequency localization operators: a geometric phase space approach”, IEEE Trans. Inform. Theory 34 (1988) 605–612.CrossRefGoogle Scholar
[2]Daubechies, I., Ten lectures on wavelets (SIAM, 1992).CrossRefGoogle Scholar
[3]Du, J. and Wong, M. W., “Traces of localization operators”, C. R. Math. Rep. Acad. Sci. Canada 22 (2000) 92–96.Google Scholar
[4]Gabor, D., “Theory of communications”, J. Inst. Elec. Eng. (London) 93 (1946) 429–457.Google Scholar
[5]Grossmann, A., Morlet, J. and Paul, T., “Transforms associated to square integrable group representations I: general results”, J. Math. Phys. 26 (1985) 2473–2479.CrossRefGoogle Scholar
[6]He, Z. and Wong, M. W., “Localization operators associated to square integrable group representations”, Panamer Math. J. 6 (1996) 93–104.Google Scholar
[7]Peierls, R., “On a minimal property of the free energy”, Phys. Rev. 54 (1938) 918–919.CrossRefGoogle Scholar
[8]Reed, M. and Simon, B., Methods of modern mathematical physics I: functional analysis, revised and enlarged ed. (Academic Press, 1980).Google Scholar
[9]Wong, M. W., Localization operators, Lecture Notes Series 47 (Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul, 1999).Google Scholar