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Media type:
E-Article
Title:
Reflection Negative Kernels and Fractional Brownian Motion
Contributor:
Jorgensen, Palle E. T.
[Author];
Neeb, Karl-Hermann
[Author];
Ólafsson, Gestur
[Author]
imprint:
OPUS FAU - Online publication system of Friedrich-Alexander-Universität Erlangen-Nürnberg, 2018-06-01
Language:
English
DOI:
https://doi.org/10.3390/sym10060191
Origination:
Footnote:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Description:
In this article we study the connection of fractional Brownian motion, representation theory and reflection positivity in quantum physics. We introduce and study reflection positivity for affine isometric actions of a Lie group on a Hilbert space E and show in particular that fractional Brownian motion for Hurst index 0<H≤1/2 is reflection positive and leads via reflection positivity to an infinite dimensional Hilbert space if 0<H<1/2 . We also study projective invariance of fractional Brownian motion and relate this to the complementary series representations of GL2(R) . We relate this to a measure preserving action on a Gaussian L2 -Hilbert space L2(E) .