Titlebook: Offbeat Integral Geometry on Symmetric Spaces; Valery V. Volchkov,Vitaly V. Volchkov Book 2013 Springer Basel 2013 Pompeiu property.harmon

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The Euclidean CaseIn many questions of integral geometry there arise operators of the following type: . This is the classical Abel transform, which can be explicitly inverted.

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Functions with Zero Ball Means on Euclidean SpaceFunctions with vanishing integrals over all balls of a fixed radius can be regarded as a generalization to the multidimensional case of periodic functions on the real line.

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Functions with Zero Integrals over PolytopesIn Chapter 4 we discussed the problem about the ball of smallest radius in which a given set . has the Pompeiu property (see the definition of .(.) in Section 4.4).

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The Pompeiu Property on a SphereIn Section 2.7 we studied the class of functions, .(..), having vanishing integrals over all closed balls of radius . lying in ...

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