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Title: A quasianalytic property of families in the image of integral transforms on higher grassmannians.

Abstract: We will consider certain integral operators on higher grassmannians that appear naturally in convex geometry, as well as in representation theory: the Radon and cosine transforms. The image of such operators is often a rather small subspace of all functions, and can be explicitly described in terms of its SO(n)-components. We will describe a quasianalytic-type property exhibited by those images, allowing to uniquely determine a function from its values on a small set. This allows us to sharpen classical uniqueness theorems of Funk and Alexandrov in geometric tomography, and of Klain and Schneider in valuation theory. Similar results hold for more general families of functions and global sections of bundles appearing as representations of GL_n(R).

Room: 4336-4384 Pav. Andr茅-Aisentadt (CRM)

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Meeting ID: 831 1853 9851

Passcode: 215516

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