# 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}
}
• D. Applebaum
• Published 3 February 2016
• Mathematics
• Forum Mathematicum
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…
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