Spherical Functions on a Semisimple Lie Group, I

1958/04/01 by Harish-Chandra, Harish-chandra Harish-Chandra · 335 citations
Mathematics · #Advanced Algebra and Geometry #Affine Lie algebra #Algebra over a field #Algebraic and Geometric Analysis #Fundamental representation #Group (periodic table) #Lie algebra #Lie group #Mathematics #Physics #Pure mathematics #Real form #Representation of a Lie group #Simple Lie group #Weight #advanced mathematical theories

paper · doi:10.2307/2372786

published in American Journal of Mathematics 80(2), 241 (JSTOR)

crossref issued 1958/04/01 · crossref published 1958/04/01 · crossref published-print 1958/04/01 · openalex publication_date 1958/04/01 · crossref created 2006/07/20 · crossref deposited 2018/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/05 · crossref indexed 2026/06/23

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• A duality for symmetric spaces with applications to group representations
• The spherical Fourier transform of rapidly decreasing functions. A simple proof of a characterization due to Harish-Chandra, Helgason, Trombi, and Varadarajan
• A quick proof of Harish-Chandra’s Plancherel theorem for spherical functions on a semisimple Lie group
• Some Conjectures for Root Systems
• Plancherel theorem for spherical functions [wikipedia]
• Zonal spherical function [wikipedia]