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boundedness of localization operators associated to left regular representations
Author(s):
M.
W.
Wong
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2911-2919.
MSC (2000):
Primary 47G10
Posted:
May 8, 2002
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Abstract:
We prove an boundedness result for localization operators associated to left regular representations of locally compact and Hausdorff groups and give an application to wavelet multipliers.
References:
- 1.
- A. L. Carey, Square integrable representations of non-unimodular groups, Bull. Austral. Math. Soc. 15 (1976), 1-12. MR 55:3153
- 2.
- I. Daubechies, Time-frequency localization operators: a geometric phase space approach, IEEE Trans. Inform. Theory 34 (1988), 605-612. CMP 21:03
- 3.
- I. Daubechies, Ten Lectures on Wavelets, SIAM, 1992. MR 93e:42045
- 4.
- M. Duflo and C. C. Moore, On the regular representation of a nonunimodular locally compact group, J. Funct. Anal. 21 (1976), 209-243. MR 52:14145
- 5.
- J. Du and M. W. Wong, Traces of localization operators, C. R. Math. Rep. Acad. Sci. Canada 22 (2000), 92-95. MR 2001c:47053
- 6.
- J. Du and M. W. Wong, Traces of wavelet multipliers, C.R. Math. Acad. Sci. Soc. R. Can. 23 (2001), 148-152.
- 7.
- G. B. Folland, A Course in Abstract Harmonic Analysis, CRC Press, 1995. MR 98c:43001
- 8.
- A. Grossmann, J. Morlet and T. Paul, Transforms associated to square integrable group representations I: general results, J. Math. Phys. 26 (1985), 2473-2479. MR 86k:22013
- 9.
- Z. He and M. W. Wong, Localization operators associated to square integrable group representations, Panamer Math. J. 6(1) (1996), 93-104. MR 97d:43009
- 10.
- Z. He and M. W. Wong, Wavelet multipliers and signals, J. Austral. Math. Soc. Ser. B 40 (1999), 437-446. MR 2001a:42040
- 11.
- H. Kumano-go, Pseudo-Differential Operators, MIT Press, 1981. MR 84c:35113
- 12.
- H. J. Landau and H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis and uncertainty II, Bell Syst. Tech. J. 40 (1961), 65-84. MR 25:4147
- 13.
- H. J. Landau and H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis and uncertainty III, Bell Syst. Tech. J. 41 (1962), 1295-1336. MR 26:5200
- 14.
- D. Slepian, On bandwidth, Proc. IEEE 64 (1976), 292-300. MR 57:2738
- 15.
- D. Slepian, Some comments on Fourier analysis, uncertainty and modeling, SIAM Rev. 25 (1983), 379-393. MR 84i:94016
- 16.
- D. Slepian and H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis and uncertainty I, Bell Syst. Tech. J. 40 (1961), 43-64. MR 25:4146
- 17.
- E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971. MR 46:4102
- 18.
- M. W. Wong, Weyl Transforms, Springer-Verlag, 1998. MR 2000c:47098
- 19.
- M. W. Wong, An Introduction to Pseudo-Differential Operators, Second Edition, World Scientific, 1999. MR 2000c:35002
- 20.
- M. W. Wong, Localization Operators, Lecture Notes Series 47, Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul, 1999. MR 2002c:22010
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Additional Information:
M.
W.
Wong
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3
Email:
mwwong@pascal.math.yorku.ca
DOI:
10.1090/S0002-9939-02-06685-6
PII:
S 0002-9939(02)06685-6
Received by editor(s):
February 21, 2001
Posted:
May 8, 2002
Additional Notes:
This research has been partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0008562
Communicated by:
David R. Larson
Copyright of article:
Copyright
2002,
American Mathematical Society
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