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, 2005/11/1518.
November 2005: 表現論シンポジウム AbstractLet 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).
