Hiroshima Mathematical Journal

An analogue of Hardy's theorem for the Harish-Chandra transform

Nobukazu Shimeno

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Abstract

A theorem of Hardy asserts that a function and its Fourier transform cannot both be very small. We prove analogues of Hardy’s theorem for the Harish- Chandra transform for spherical functions on a non-compact semisimple Lie group and the Helgason transform on a Riemannian symmetric space of the non-compact type.

Article information

Source
Hiroshima Math. J., Volume 31, Number 3 (2001), 383-390.

Dates
First available in Project Euclid: 23 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1151105726

Digital Object Identifier
doi:10.32917/hmj/1151105726

Mathematical Reviews number (MathSciNet)
MR1870982

Zentralblatt MATH identifier
0999.22011

Subjects
Primary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]
Secondary: 22E46: Semisimple Lie groups and their representations

Citation

Shimeno, Nobukazu. An analogue of Hardy's theorem for the Harish-Chandra transform. Hiroshima Math. J. 31 (2001), no. 3, 383--390. doi:10.32917/hmj/1151105726. https://projecteuclid.org/euclid.hmj/1151105726


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