Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Matrix-exponential groups and Kolmogorov–Fokker–Planck equations

Matrix-exponential groups and Kolmogorov–Fokker–Planck equations Aim of this paper is to provide new examples of Hörmander operators $${\mathcal{L}}$$ to which a Lie group structure can be attached making $${\mathcal{L}}$$ left invariant. Our class of examples contains several subclasses of operators appearing in literature and arising both in theoretical and in applied fields: evolution Kolmogorov operators, degenerate Ornstein–Uhlenbeck operators, Mumford and Fokker–Planck operators, Ornstein–Uhlenbeck operators with time-dependent periodic coefficients. Our examples basically come from exponential of matrices, as well as from linear constant-coefficient ODE’s, in $${\mathbb{R}}$$ or in $${\mathbb{C}}$$ . Furthermore, we describe how these groups can be combined together to obtain new structures and new operators, also having an interest in the applied field. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

Matrix-exponential groups and Kolmogorov–Fokker–Planck equations

Loading next page...
 
/lp/springer-journals/matrix-exponential-groups-and-kolmogorov-fokker-planck-equations-7rlQ3gy1eQ

References (27)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Basel AG
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-011-0123-1
Publisher site
See Article on Publisher Site

Abstract

Aim of this paper is to provide new examples of Hörmander operators $${\mathcal{L}}$$ to which a Lie group structure can be attached making $${\mathcal{L}}$$ left invariant. Our class of examples contains several subclasses of operators appearing in literature and arising both in theoretical and in applied fields: evolution Kolmogorov operators, degenerate Ornstein–Uhlenbeck operators, Mumford and Fokker–Planck operators, Ornstein–Uhlenbeck operators with time-dependent periodic coefficients. Our examples basically come from exponential of matrices, as well as from linear constant-coefficient ODE’s, in $${\mathbb{R}}$$ or in $${\mathbb{C}}$$ . Furthermore, we describe how these groups can be combined together to obtain new structures and new operators, also having an interest in the applied field.

Journal

Journal of Evolution EquationsSpringer Journals

Published: Mar 1, 2012

There are no references for this article.