Banach Journal of Mathematical Analysis

On positive definite distributions with compact support

Saulius Norvidas

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Abstract

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

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

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1419001700

Digital Object Identifier
doi:10.15352/bjma/09-3-2

Mathematical Reviews number (MathSciNet)
MR3296122

Zentralblatt MATH identifier
1325.46046

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.bjma/1419001700


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