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- Title
The Plancherel formula of Fourier integral operators: The case of Sp(1,1).
- Authors
Jia, Xiaoke; Fan, Xingya
- Abstract
In this paper, we consider the Plancherel formula for Fourier integral operator on the space L 2 (ℍ 2) , where ℍ is the quaternion skew field. By using the metaplectic representations of a noncompact classical dual pair (S O ∗ (4) , S p (1 , 1)) and combining with the Plancherel formula of Poisson transform, we obtain the direct integral decomposition of all irreducible unitary representations of Fourier integral operator.
- Subjects
INTEGRAL operators; FOURIER integrals; DIVISION rings; INTEGRAL representations; INTEGRAL transforms; QUATERNIONS
- Publication
International Journal of Wavelets, Multiresolution & Information Processing, 2024, Vol 22, Issue 2, p1
- ISSN
0219-6913
- Publication type
Article
- DOI
10.1142/S021969132350042X