Journal article
Reflection Negative Kernels and Fractional Brownian Motion
Symmetry (Basel), Vol.10(6), p.191
06/01/2018
DOI: 10.3390/sym10060191
Abstract
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 epsilon 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 GL(2) (R). We relate this to a measure preserving action on a Gaussian L-2-Hilbert space L-2 (epsilon).
Details
- Title: Subtitle
- Reflection Negative Kernels and Fractional Brownian Motion
- Creators
- Palle E. T Jorgensen - Univ Iowa, Dept Math, Iowa City, IA 52242 USAKarl-Hermann Neeb - FAU Erlangen Nurnberg, Dept Math, Cauerstr 11, D-91058 Erlangen, GermanyGestur Olafsson - Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
- Resource Type
- Journal article
- Publication Details
- Symmetry (Basel), Vol.10(6), p.191
- DOI
- 10.3390/sym10060191
- ISSN
- 2073-8994
- eISSN
- 2073-8994
- Publisher
- MDPI
- Number of pages
- 39
- Language
- English
- Date published
- 06/01/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9984241058202771
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