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.
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Bonfiglioli, A., Lanconelli, E. Matrix-exponential groups and Kolmogorov–Fokker–Planck equations. J. Evol. Equ. 12, 59–82 (2012). https://doi.org/10.1007/s00028-011-0123-1
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DOI: https://doi.org/10.1007/s00028-011-0123-1