An analogue of the Fuglede formula in integral geometry on matrix spaces

Details An analogue of the Fuglede formula in integral geometry on matrix spaces An analogue of the Fuglede formula in integral geometry on matrix spaces

2004-01-13

arxiv.org/abs/math/0401127v1

Mathematics

Functional Analysis

AMS LaTeX, 20 pages

Scientific paper

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.

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