IJPAM: Volume 25, No. 1 (2005)

THE LEVY-KHINTCHINE REPRESENTATIONS AND
FUNCTIONAL ALGEBRAS OF TEST FUNCTIONS

Vladimir Volkovich Zeev$^{1}$Software Engineering Department, ORT Braude College, P.O. Box 21982, Karmiel, 21982, ISRAEL, Barzily Zeev$^{2}$, Peter Soreanu$^{3}$
$^{1,2,3}$Software Engineering Department
ORT Braude College
P.O. Box 21982, Karmiel, 21982, ISRAEL
$^1$Department of Mathematics and Statistics
The University of Maryland
Baltimore County, USA
$^1$e-mail: vlvolkov@ort.org.il
$^2$e-mail: zbarzily@ort.org.il
$^3$e-mail: psoreanu@ort.org.il


Abstract.We discuss a new approach for the proof of the Levy-Khintchine formula for the $V$-infinitely divisible laws. Our proof is based on a description of the conditionally positive definite functions as positive functionals on semi-normed algebras of suitable test functions. In the framework of this approach we obtain integral representations of the common continuous positive definite functions and the logarithms of characteristic functions of the ordinary infinitely divisible and $V$-infinitely divisible distribution.

Received: October 7, 2005

AMS Subject Classification: 60E07, 62E10, 42A99, 65D05

Key Words and Phrases: infinitely divisible distribution, $V$-infinitely divisible distribution, positive definite function, Levy-Khintchine formula, conditionally positive definite functions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 1