# Probabilistic trace and Poisson summation formulae on locally compact abelian groups

@article{Applebaum2016ProbabilisticTA, title={Probabilistic trace and Poisson summation formulae on locally compact abelian groups}, author={David Applebaum}, journal={Forum Mathematicum}, year={2016}, volume={29}, pages={1499 - 1500} }

We investigate convolution semigroups of probability measures with continuous densities on locally compact abelian groups, which have a discrete subgroup such that the factor group is compact. Two interesting examples of the quotient structure are the $d$--dimensional torus, and the adelic circle. Our main result is to show that the Poisson summation formula for the density can be interpreted as a probabilistic trace formula, linking values of the density on the factor group to the trace of the…

## 4 Citations

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