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On the coefficients of an asymptotic expansion of spherical functions on symmetric spaces

Authors: John J. H. Miller and D. J. Simms
Journal: Proc. Amer. Math. Soc. 37 (1973), 448-452
MSC: Primary 43A90; Secondary 22E30
MathSciNet review: 0312159
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Abstract: The asymptotic expansion of a spherical function on a symmetric space of noncompact type, obtained by Harish-Chandra, is a finite linear combination of expansions of the form $ {\Phi _\theta } = {\sum _\mu }'{\Gamma _\mu }(\theta ){e^{\theta - \mu }}$. In this paper it is proved that $ {\lim _{t \to \infty }}'{\Gamma _\mu }(te - \bar \rho )$ is finite and rational for any e, where $ \bar \rho $ is the restriction of half the sum of the positive roots.

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Keywords: Symmetric space of noncompact type, spherical function, coefficient of asymptotic expansion, radial limit
Article copyright: © Copyright 1973 American Mathematical Society

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