Weyl Group Invariants and Application to Spherical Harmonic Analysis on Symmetric Spaces

2009/01/29 by Olafsson, Gestur, Wolf, Joseph A. · 1 citation
Mathematics · #22E46 #43A85 #53C35 #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0901.4765

openalex publication_date 2009/01/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion that ensure that the restriction of invariant polynomials to subspaces is surjective. We apply our criterion to problems in Fourier analysis on projective/injective limits, specifically to theorems of Paley--Wiener type.

Citations

• Infinite Dimensional Multiplicity Free Spaces III: Matrix Coefficients and Regular Functions

Cited by

• The Paley-Wiener Theorem and Limits of Symmetric Spaces

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