The Plancherel formula of Fourier integral operators: The case of Sp(1,1)

DOI10.1142/s021969132350042xOpenAlexW4385782370MaRDI QIDQ6201198

Unnamed Author, Xingya Fan

Publication date: 20 February 2024

Published in: International Journal of Wavelets, Multiresolution and Information Processing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s021969132350042x

zbMATH Keywords

Plancherel formulaFourier integral operatorPoisson transform

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Pseudodifferential and Fourier integral operators on manifolds (58J40) Other transforms and operators of Fourier type (43A32)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Realization of quaternionic discrete series on the unit ball in \(\mathbb H^d\)
• Non-Abelian harmonic analysis. Applications of \(SL(2,{\mathbb{R}})\)
• On the Segal-Shale-Weil representations and harmonic polynomials
• Eigenspaces of the Laplacian on hyperbolic spaces: composition series and integral transforms
• The explicit duality correspondence of (\(\text{Sp}(p,q),\text{O}^{*}(2n)\))
• \(L^ 2\)-versions of the Howe correspondence. II
• Generalized Fourier transforms associated with the oscillator representation
• Fourier integral operators. I
• Holomorphic discrete series for the real symplectic group
• On the Howe correspondence for symplectic-orthogonal dual pairs
• Transcending Classical Invariant Theory
• Quaternionic discrete series for $Sp(1,1)$
• Remarks on Classical Invariant Theory
• On quaternionic discrete series representations, and their continuations.
• Harmonic Analysis in Phase Space. (AM-122)
• Multivariable Orthogonal Polynomials and Coupling Coefficients for Discrete Series Representations
• $L^2$-versions of the Howe correspondence I.
• Homogeneous functions on light cones: the infinitesimal structure of some degenerate principal series representations
• Branching of metaplectic representation of 𝑆𝑝(2,ℝ) under its principal 𝕊𝕃(2,ℝ)-subgroup

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