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We prove that certain quotients of entire functions are characteristicfunctions. Under some conditions, the probability measure corresponding to acharacteristic function of that type has a density which can be expressed as ageneralized Dirichlet series, which in turn is an infinite linear combinationof exponential or Laplace densities. These results are applied to severalexamples.

Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities