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The spherical mean
value operator for compact symmetric spaces
Vishwambhar Pati, Mehrdad Mirshams Shahshahani and Alladi Sitaram |
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Vol. 168 (1995), No. 2, 335–344
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Abstract |
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When M is a compact symmetric space, the spherical mean value operator Lr (for a fixed r > 0) acting on L2(M) is considered. The eigenvalues λ for Lrf = λf are explicitly determined in terms of the elementary spherical functions associated with the symmetric space. Alternative proofs are also provided for some results of T. Sunada regarding the special eigenvalues +1 and −1 using a purely harmonic analytic point of view. |
Mathematical Subject Classification 2000
Primary: 58G15
Secondary: 22E46, 43A90, 58G25
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Milestones
Received: 1 October 1992
Published: 1 April 1995
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Authors |
| Vishwambhar Pati | |
| Mehrdad Mirshams Shahshahani | |
| Alladi Sitaram | |
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