Characteristic functions as distributional boundary values of analytic functions in tube domains |
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Authors: | Saulius Norvidas |
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Institution: | 1. Institute of Mathematics and Informatics, Vilnius University, Akademijos str. 4, LT-08663, Vilnius, Lithuania 2. Mykolas Romeris University, Ateities str. 20, LT-08303, Vilnius, Lithuania
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Abstract: | We propose necessary and sufficient conditions for a complex-valued function f on \( {{\mathbb{R}}^n} \) to be a characteristic function of a probability measure. Certain analytic extensions of f to tubular domains in \( {{\mathbb{C}}^n} \) are studied. In order to extend the class of functions under study, we also consider the case where f is a generalized function (distribution). The main result is given in terms of completely monotonic functions on convex cones in \( {{\mathbb{R}}^n} \) . |
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