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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0312159-9
PII: S 0002-9939(1973)0312159-9
Keywords: Symmetric space of noncompact type, spherical function, coefficient of asymptotic expansion, radial limit
Article copyright: © Copyright 1973 American Mathematical Society