Sigurdur Helgason

His research interests were in geometric analysis on homogeneous spaces particularly symmetric spaces. He defined and developed a natural geometric Fourier transform on the latter spaces and applied this theory to invariant differential operators. This concerns both the study of general features like solvability questoins, eigenfuntions and eigenspace representations as well as investigation of specific equations lke the wave equation and its generalizatoin to multidimensional time. He also defined the Radon transform for a double fibration of a homogeneous space and investigated its operational properties for a variety of cases, including a horocycle and geodesic submanifolds in a symmetric space.