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QUALITATIVE UNCERTAINTY PRINCIPLE ON CERTAIN LIE GROUPS

Part of: Harmonic analysis in one variable Integral transforms, operational calculus

Published online by Cambridge University Press:  18 December 2023

ARUP CHATTOPADHYAY ,
DEBKUMAR GIRI Open the ORCID record for DEBKUMAR GIRI [Opens in a new window]  and
R. K. SRIVASTAVA Open the ORCID record for R. K. SRIVASTAVA [Opens in a new window]
ARUP CHATTOPADHYAY
Affiliation:
Department of Mathematics, Indian Institute of Technology, Guwahati 781039, India e-mail: arupchatt@iitg.ac.in
DEBKUMAR GIRI
Affiliation:
School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, An OCC of Homi Bhabha National Institute, Jatni 752050, India e-mail: debkumarg@niser.ac.in
R. K. SRIVASTAVA*
Affiliation:
Department of Mathematics, Indian Institute of Technology, Guwahati 781039, India
*
e-mail: rksri@iitg.ac.in
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Abstract

In this article, we study the recent development of the qualitative uncertainty principle on certain Lie groups. In particular, we consider that if the Weyl transform on certain step-two nilpotent Lie groups is of finite rank, then the function has to be zero almost everywhere as long as the nonvanishing set for the function has finite measure. Further, we consider that if the Weyl transform of each Fourier–Wigner piece of a suitable function on the Heisenberg motion group is of finite rank, then the function has to be zero almost everywhere whenever the nonvanishing set for each Fourier–Wigner piece has finite measure.

Keywords

Heisenberg groupFourier transformHermite functionsqualitative uncertainty principle

MSC classification

Primary: 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Secondary: 44A35: Convolution
Type
Research Article
Information
Journal of the Australian Mathematical Society , First View , pp. 1 - 19
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by Ji Li

D.G. acknowledges the support provided by IIT Guwahati, Government of India.

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