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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 of Evolution Equations – Springer Journals
Published: Mar 1, 2012
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