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A RESULT OF PALEY AND WIENER ON DAMEK–RICCI SPACES

Part of: Lie groups Abstract harmonic analysis

Published online by Cambridge University Press:  03 May 2019

MITHUN BHOWMIK
MITHUN BHOWMIK*
Affiliation:
Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India
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Abstract

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A classical result due to Paley and Wiener characterizes the existence of a nonzero function in $L^{2}(\mathbb{R})$, supported on a half-line, in terms of the decay of its Fourier transform. In this paper, we prove an analogue of this result for Damek–Ricci spaces.

Keywords

Damek–Ricci spaceFourier transformPaley–Wiener theorem

MSC classification

Primary: 22E30: Analysis on real and complex Lie groups
Secondary: 43A85: Analysis on homogeneous spaces

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 109 , Issue 1 , August 2020 , pp. 1 - 16
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Copyright
© 2019 Australian Mathematical Publishing Association Inc.

Footnotes

The author was supported by Research Fellowship from Indian Statistical Institute, India.

†

Current address: Department of Mathematics, Indian Institute of Technology, Bombay, Powai, Mumbai-400076, India email mithunbhowmik123@gmail.com, mithun@math.iitb.ac.in

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