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An analogue of the Fuglede formula in integral geometry on matrix spaces. (English) Zbl 1088.44500

Agranovsky, Mark (ed.) et al., Complex analysis and dynamical systems II. Proceedings of the 2nd conference in honor of Professor Lawrence Zalcman’s sixtieth birthday, Nahariya, Israel, June 9–12, 2003. Providence, RI: American Mathematical Society (AMS); Ramat Gan: Bar-Ilan University (ISBN 0-8218-3709-5/pbk). Contemporary Mathematics 382. Israel Mathematical Conference Proceedings, 305-320 (2005).
Summary: The well-known formula of B. Fuglede [Math. Scad. 6, 207–212 (1958; Zbl 0088.14702)] expresses the mean value of the Radon \(k\)-plane transform on \(\mathbb{R}^n\) as a Riesz potential. We generalize this formula for the space of \(n\times m\) real matrices and show that the corresponding matrix \(k\)-plane transform \(f\to\widehat f\) is injective if and only if \(n- k\geq m\). Various 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.
For the entire collection see [Zbl 1078.37001].

MSC:

44A12 Radon transform

Citations:

Zbl 0088.14702
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