The Plancherel formula of Fourier integral operators: The case of Sp(1,1)
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Published:2023-08-31
Issue:02
Volume:22
Page:
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ISSN:0219-6913
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Container-title:International Journal of Wavelets, Multiresolution and Information Processing
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language:en
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Short-container-title:Int. J. Wavelets Multiresolut Inf. Process.
Author:
Jia Xiaoke1,
Fan Xingya1ORCID
Affiliation:
1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
Abstract
In this paper, we consider the Plancherel formula for Fourier integral operator on the space [Formula: see text], where [Formula: see text] is the quaternion skew field. By using the metaplectic representations of a noncompact classical dual pair [Formula: see text] and combining with the Plancherel formula of Poisson transform, we obtain the direct integral decomposition of all irreducible unitary representations of Fourier integral operator.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Xinjiang
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Information Systems,Signal Processing