Processes of flats induced by higher dimensional processes III |
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Authors: | Paul Goodey Ralph Howard Mark Reeder |
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Affiliation: | (1) Department of Mathematics, University of Oklahoma, 73019 Norman, OK, USA;(2) Department of Mathematics, University of South Carolina, 29208 Columbia, SC, USA |
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Abstract: | Stationary processes of k-flats in d can be thought of as point processes on the Grassmannian kd of k-dimensional subspaces of d. 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 kd. 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.The research of the first and third authors was supported in part by NSF grants DMS-9207019 and DMS-9304284. The research of the second author was supported in part by NFR contract number R-RA 4873-306 and the Swedish Academy of Sciences. |
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Keywords: | 60D05 52A22 |
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