外尔群不变量及其在对称空间球调和分析中的应用
Weyl Group Invariants and Application to Spherical Harmonic Analysis on Symmetric Spaces
摘要：
多项式不变量是李群和对称空间分析的基本对象。对称空间上的不变微分算子用外尔群不变多项式描述.本文给出了一个简单的判据，它保证了不变多项式对子空间的限制是满射的。我们应用我们的标准，在傅里叶分析的问题投影/内射的限制，特别是佩利-维纳型定理。
英文摘要：
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.
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