An analogue of Hardy’s theorem for semi-simple Lie groups
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- by J. Sengupta PDF
- Proc. Amer. Math. Soc. 128 (2000), 2493-2499 Request permission
Abstract:
A well known theorem of Hardy on Fourier transform pairs says that a function $f$ on ${\mathbf R}^n$ and its Fourier transform $\stackrel {\wedge }{f}$ cannot both be “very rapidly decreasing”. We prove here an analogue of this result in the case of semi-simple Lie groups.References
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Additional Information
- J. Sengupta
- Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai - 400 005, India
- Email: sengupta@math.tifr.res.in
- Received by editor(s): July 16, 1998
- Received by editor(s) in revised form: September 16, 1998
- Published electronically: February 25, 2000
- Communicated by: Roe Goodman
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2493-2499
- MSC (1991): Primary 22E30; Secondary 22E46, 43A30
- DOI: https://doi.org/10.1090/S0002-9939-00-05258-8
- MathSciNet review: 1654100