OPERATIONS ON CONSTRUCTIBLE FUNCTIONS

[摘要] A constructible function phi on a real analytic manifold X is a Z-valued function such that the partition X = box-with-top-missing m is-an-element-of Z-phi-1(m) is a subanalytic stratification. Here, we define new operations on constructible functions (inverse or direct images, duality) and prove some theorems related to these operations (e.g., duality commutes to direct image). As an application we solve the convolution equation phi * psi = delta, when phi is the characteristic function of a convex compact set. This problem which seems to have some utility in robotics, was first considered by Guibas et al. and this paper may be considered as a new approach, and an extension to higher dimension of the material contained in their paper.

[发布日期] 1991-07-01