This is an announcement for the paper "An analogue of the Fuglede formula in integral geometry on matrix spaces" by E.Ournycheva and B.Rubin.
Abstract: The well known formula of B. Fuglede expresses the mean value of the Radon k-plane transform on $R^n$ as a Riesz potential. We extend this formula to the space of $n \times m$ real matrices and show that the corresponding matrix k-plane transform $f \to \hat f$ is injective if and only if $n-k \ge m$. Different inversion formulas for this transform are obtained. We assume that $f \in L^p$ or $f$ is a continuous function satisfying certain "minimal" conditions at infinity.
Archive classification: Functional Analysis
Mathematics Subject Classification: Primary 44A12; Secondary 47G10
Remarks: AMS LaTeX, 20 pages
The source file(s), Fug8.tex: 50342 bytes, is(are) stored in gzipped form as 0401127.gz with size 18kb. The corresponding postcript file has gzipped size 82kb.
Submitted from: ournyce@math.huji.ac.il
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