On Closed Ideals in the Motion Group Algebra.
On a generalized asymptotic mean value property.
On Schwartz's theorem for the motion group
Schwartz’s Theorem in spectral synthesis of continuous functions on the real is generalized to the Euclidean motion group. The rightsided analogue of Schwartz’s Theorem for the motion group is reduced to the study of some invariant subspaces of continuous functions on .
Multipliers on Schwartz spaces of some Lie groups
Schwartz's theorem on mean periodic vector-valued functions
Harmonic analysis of spherical functions on
Denote by the algebra of spherical integrable functions on , with convolution as multiplication. This is a commutative semi-simple algebra, and we use its Gelfand transform to study the ideals in . In particular, we are interested in conditions on an ideal that ensure that it is all of , or that it is . Spherical functions on are naturally represented as radial functions on the unit disk in the complex plane. Using this representation, these results are applied to characterize harmonic...
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