Distributional boundary values of analytic functions and positive definite distributions - Norvidas, Saulius (Nonlinear Analysis: Modelling and Control, 2015)
We propose necessary and sufficient conditions for a distribution (generalized function) fof several variables to be positive definite. For this purpose, certain analytic extensions of f to tubular domains in complex space Cn are studied. The main result is given in terms of the Cauchy transform and completely monotonic functions.