Analytic and group-theoretic aspects of the Cosine transform

Gestur Olafsson (1) , Angela Pasquale (2) , Boris Rubin (1)

1 LSU - Louisiana State University
2 IECL - Institut Élie Cartan de Lorraine

This is a brief survey of recent results by the authors devoted to one of the most important operators of integral geometry. Basic facts about the analytic family of cosine transforms on the unit sphere in R n and the corresponding Funk transform are extended to the " higher-rank " case for functions on Stiefel and Grassmann manifolds. Among the topics we consider are the analytic continuation and the structure of the polar sets, the connection with the Fourier transform on the space of rectangular matrices, inversion formulas and spectral analysis, and the group-theoretic realization as an intertwining operator between generalized principal series representations of SL(n, R).

Domaines: Mathématiques [math]

Gestur Olafsson, Angela Pasquale, Boris Rubin. Analytic and group-theoretic aspects of the Cosine transform. Contemporary mathematics, 2013, Geometric Analysis and Integral Geometry, 584, pp.167-188. ⟨10.1090/conm/598/12009⟩. ⟨hal-01281896⟩