On Hull-Minimal Ideals in the Schwartz Algebras of Spherical Functions on a Semi-Simple Lie Group

Bassey, U. N. ; Oyadare, O. O. (2011)


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 r-spherical functions on G, we characterize the hullminimal ideals in terms of the cusp forms.