Aim of this paper is to provide new examples of Hörmander operators L to which a Lie group structure can be attached making 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, aswell as from linear constant-coefficient ODE’s, in R or in 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.

Matrix exponential groups and Kolmogorov-Fokker-Planck equations

BONFIGLIOLI, ANDREA;LANCONELLI, ERMANNO
2012

Abstract

Aim of this paper is to provide new examples of Hörmander operators L to which a Lie group structure can be attached making 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, aswell as from linear constant-coefficient ODE’s, in R or in 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.
2012
A. Bonfiglioli; E. Lanconelli
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/110484
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