Let $f$ be a non-negative square-integrable function on a finite volume hyperbolic surface $\Gamma\backslash\mathbb{H}$, and assume that $f$ is non-autocorrelated, that is, perpendicular to its image under the operator of averaging over the circle of a fixed radius $r$. We show that in this case the support of $f$ is small, namely, it satisfies $\mu(supp{f}) \leq (r+1)e^{-\frac{r}{2}} \mu(\Gamma\backslash\mathbb{H})$... (read more)

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