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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

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measure of Haar

Let $(G,K)$ be a Gelfand pair. Why, for a function $f$ $K$-binvariant with respect to a compact subgroup $K$ of a group $G$, do we have the following equality: $$ f(xy) = \int_K f(xky) \, dk$$ A funct …