International Journal of Functional Analysis, Operator Theory and Applications
Volume 3, Issue 1, Pages 37 - 52
(June 2011)
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ON HULL-MINIMAL IDEALS IN THE SCHWARTZ ALGEBRAS OF SPHERICAL FUNCTIONS
ON A SEMI-SIMPLE LIE GROUP
U. N. Bassey and O. O. Oyadare
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Abstract:
The hull-minimal
ideals are discussed for the Harish-Chandra Schwartz algebra of a connected
semi-simple Lie group G. In
particular, we construct the basis elements for these ideals, and, when
restricted to the Schwartz algebra of t-spherical functions on G, we characterize the hull-minimal ideals in terms of the cusp
forms. |
| Keywords and phrases: hull-minimal ideal, Schwartz algebra, spherical function, semi-simple Lie group. |
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