Positivity, ( ISI ), Volume (25), No (2), Year (2020-6) , Pages (515-530)

Title : ( Kolmogorov decomposition of conditionally completely positive definite kernels )

Authors: mostafa ghaemi , Mohammad Sal Moslehian , Qingxiang Xu ,

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Abstract

In this paper, we investigate conditionally completely positive definite kernels in the setting of Hilbert C∗-modules. At first, we present a correspondence between conditionally completely positive definite kernels and completely positive definite kernels. Utilizing this relation, we give the Kolmogorov decomposition for a certain conditionally completely positive definite kernel. We present a characterization of conditionally completely positive definite kernels majorized by a kernel under some mild conditions. Finally, as an application of this decomposition, we find a sufficient condition for the existence of an extreme point of a convex set consisting of some special kernels.

Keywords

Kolmogorov decomposition Completely positive definite kernel Conditionally completely positive definite kernel Extreme point
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@article{paperid:1082227,
author = {Ghaemi, Mostafa and Sal Moslehian, Mohammad and Qingxiang Xu},
title = {Kolmogorov decomposition of conditionally completely positive definite kernels},
journal = {Positivity},
year = {2020},
volume = {25},
number = {2},
month = {June},
issn = {1385-1292},
pages = {515--530},
numpages = {15},
keywords = {Kolmogorov decomposition Completely positive definite kernel Conditionally completely positive definite kernel Extreme point},
}

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%0 Journal Article
%T Kolmogorov decomposition of conditionally completely positive definite kernels
%A Ghaemi, Mostafa
%A Sal Moslehian, Mohammad
%A Qingxiang Xu
%J Positivity
%@ 1385-1292
%D 2020

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