Processes of Flats Induced by Higher Dimensional Processes Iii

Department of Mathematics, University of Oklahoma, Norman, OK 73019 Department of Mathematics, University of South Carolina, Columbia, SC 29208 Department of Mathematics, University of Oklahoma, Norman, OK 73019 Abstract. Stationary processes of k-flats in Ed can be thought of as point processes on the Grassmannian L k of k-dimensional subspaces of Ed . If such a process is sampled by a (d − k + j)-dimensional space F , it induces a process of j-flats in F . In this work we will investigate the possibility of determining the original k-process from knowledge of the intensity measures of the induced j-processes. We will see that this is impossible precisely when 1 < k < d− 1 and j = 0, . . . , 2 r 2 − 1, where r is the rank of the manifold L k . We will show how the problem is equivalent to the study of the kernel of various integral transforms, these will then be investigated using harmonic analysis on Grassmannian manifolds.