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A Generalization of a Theorem by Bochner

A Generalization of a Theorem by Bochner

A theorem of Bochner states that if $\mu$ is a complex Borel measure on the $n$-dimensional torus ${{\mathbf {T}}^n}$ with Fourier-coefficients that vanish outside a proper cone in ${{\mathbf {Z}}^n}$, then $\mu$ is absolutely continuous with respect to Haar measure on ${{\mathbf {T}}^n}$. This result is generalized to a ${C^ …