Banach Journal of Mathematical Analysis

On positive definite distributions with compact support

Saulius Norvidas

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We propose necessary and sufficient conditions for a distribution (generalized function) $f$ of several variables to be positive definite. For this purpose, certain analytic extensions of $f$ to tubular domains in complex space $\mathbb{C}^n$ are studied. The main result is given in terms of completely monotonic functions on convex cones in $\mathbb{R}^n$.

Article information

Banach J. Math. Anal., Volume 9, Number 3 (2015), 14-23.

First available in Project Euclid: 19 December 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46F20: Distributions and ultradistributions as boundary values of analytic functions [See also 30D40, 30E25, 32A40]
Secondary: 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Positive definite distributions analytic representations of distributions Cauchy transform completely monotonic functions convex cones


Norvidas , Saulius. On positive definite distributions with compact support. Banach J. Math. Anal. 9 (2015), no. 3, 14--23. doi:10.15352/bjma/09-3-2.

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