A RANGE CHARACTERIZATION OF TOPOLOGICAL RADON TRANSFORMS ON GRASSMANN MANIFOLDS
The analytic Radon transformation is one of the most important integral transformations in mathematics, which is applied to the CT scan, partial differential equations and so on. In this paper, we study its topological analogy. In our theory, the integral is based on the topological Euler characteristics of subanalytic subsets (see [8, 16] etc. Recently, the topological Radon transformation is applied to class formulas for dual varieties in algebraic geometry, sensor networks in applied mathematics and so on (see [1] [10 12] etc. We denote the eld of real numbers or that of complex numbers by K (i.e. K R or C) We also denote by FN (k) the Grassmann manifold consisting of k dimensional linear subspaces in KN Let p, q be positive integers satisfying p q, set X FN (p) and Y FN (q) Let us also set Sp (x, y) X x Y x y} which is an incidence submanifold of X x Y and consider the diagram: X x Y