Transformation de Fourier spherique des espaces de Schwartz

DOI10.1016/0022-1236(80)90040-3zbMath0507.43002OpenAlexW2058574650MaRDI QIDQ1837360

Jean-Louis Clerc

Publication date: 1980

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(80)90040-3

zbMATH Keywords

polynomial growthspherical functionsholomorphic functionexponential decaycomplex interpolationpolynomial decaySchwartz spacesspherical Fourier transformnoncompact symmetric spacebiinvariantrapidly decreasing

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Semisimple Lie groups and their representations (22E46) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30) Analysis on other specific Lie groups (43A80) Harmonic analysis and spherical functions (43A90)

Related Items

Norms of zonal spherical functions and Fourier series on compact symmetric spaces, Paley-Wiener type theorems on harmonic extensions of \(H\)-type groups, \(L^{p}\)-Fourier analysis for certain differential-reflection operators, The spherical Fourier transform of rapidly decreasing functions. A simple proof of a characterization due to Harish-Chandra, Helgason, Trombi, and Varadarajan, \(L^ p\)-\(L^ q\) estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. I

Cites Work

• Unnamed Item
• On the tensor product of a finite and an infinite dimensional representation
• Prolongements de foncteurs d'interpolation et applications
• An analogue of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces
• Representation of complex semi-simple Lie groups and Lie algebras
• Spherical transforms on semisimple Lie groups
• On the Plancherel formula and the Paley-Wiener theorem for spherical functions on semisimple Lie groups
• Spherical Functions on a Semisimple Lie Group, I
• A Quick Proof of Harish-Chandra's Plancherel Theorem for Spherical Functions on a Semisimple Lie Group
• Elementary spherical functions on symmetric spaces.