Dept. Math, Hokkaido Univ. EPrints Server

錐上に台をもつ関数のラドン変換について (Radon transform of a function supported on a cone)

真野, 元 錐上に台をもつ関数のラドン変換について (Radon transform of a function supported on a cone). In: 表現論シンポジウム, 2005/11/15-18.

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November 2005: 表現論シンポジウム

Abstract

Let C := {x ∈ Rp+q \ {0} : Q(x) = 0} be the conical subvariety in Rp+q associated to a quadratic form Q(x) := x_1^2 + · · · + x_p^2 − x^2_p+1 − · · · − x^2_p+q. We regard C^∞_0 (C) as a subspace of distributions on R^p+q with compact support contained in C. This talk will concern with the image of C^∞_0 (C) under the Radon transform R, particularly, with the singularity of (Rf)(ξ, t) at t = 0. The differentiability of (Rf)(ξ, t) at t = 0 is closely connected to the analysis on the minimal unitary representation of the indefinite orthogonal group O(p+ 1, q + 1).

Item Type:Conference or Workshop Item (UNSPECIFIED)
Subjects:16-xx ASSOCIATIVE RINGS AND ALGEBRAS
ID Code:822