On an analytic description of the α-cosine transform on real Grassmannians

Author:

Alesker Semyon1,Gourevitch Dmitry2,Sahi Siddhartha3

Affiliation:

1. Department of Mathematics, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel

2. Faculty of Mathematics and Computer Science, Weizmann Institute of Science, P.O. Box 26, Rehovot 76100, Israel

3. Department of Mathematics, Rutgers University, Hill Center - Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA

Abstract

The goal of this paper is to describe the [Formula: see text]-cosine transform on functions on real Grassmannian [Formula: see text] in analytic terms as explicitly as possible. We show that for all but finitely many complex [Formula: see text] the [Formula: see text]-cosine transform is a composition of the [Formula: see text]-cosine transform with an explicitly written (though complicated) [Formula: see text]-invariant differential operator. For all exceptional values of [Formula: see text] except one, we interpret the [Formula: see text]-cosine transform explicitly as either the Radon transform or composition of two Radon transforms. Explicit interpretation of the transform corresponding to the last remaining value [Formula: see text], which is [Formula: see text], is still an open problem.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

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