The principal investigator will study range and kernel properties of various examples of Radon transformations. He will further analyze relationships between the algebras of invariant differential operators on symmetric spaces and bi-invariant differential operators on the isometry group. A second investigator will study unipotent representations, particularly their unitary character as well as the relationship of these representations to Dixmier algebras and their characters. Two investigators will study problems related to the theory of differential operators. An operator is a function from one set back to itself. In this case these sets are themselves collections of functions. Specifically, differential operators carry functions to their derivatives. These investigators will use ideas from both analysis and geometry to extend their understanding of these and other operators.
