This is an announcement for the paper "Composite cosine transforms" by E. Ournycheva and B. Rubin.
Abstract: The cosine transforms of functions on the unit sphere play an important role in convex geometry, the Banach space theory, stochastic geometry and other areas. Their higher-rank generalization to Grassmann manifolds represents an interesting mathematical object useful for applications. We introduce more general integral transforms that reveal distinctive features of higher-rank objects in full generality. We call these new transforms the composite cosine transforms, by taking into account that their kernels agree with the composite power function of the cone of positive definite symmetric matrices. We show that injectivity of the composite cosine transforms can be studied using standard tools of the Fourier analysis on matrix spaces. In the framework of this approach, we introduce associated generalized zeta integrals and give new simple proofs to the relevant functional relations. Our technique is based on application of the higher-rank Radon transform on matrix spaces.
Archive classification: Functional Analysis
Mathematics Subject Classification: Primary 42B10; Secondary 52A22
Remarks: 15 pages
The source file(s), ctb12.tex: 51867 bytes, is(are) stored in gzipped form as 0607224.gz with size 18kb. The corresponding postcript file has gzipped size 80kb.
Submitted from: ournyche@math.kent.edu
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