Semiclassical Analysis for the Kramers–Fokker–Planck Equation

ABSTRACT On étudie des estimations semiclassiques sur la résolvente d'opérateurs qui ne sont ni elliptiques ni autoadjoints, que l'on utilise pour étudier le problème de Cauchy. En particulier on obtient une description précise du spectre pres de l'axe imaginaire, et des estimations de résolvente à l'intérieur du pseudo-spectre. On applique ensuite les résultats à l'opérateur de Kramers–Fokker–Planck. We study some accurate semiclassical resolvent estimates for operators that are neither selfadjoint nor elliptic, and applications to the Cauchy problem. In particular we get a precise description of the spectrum near the imaginary axis and precise resolvent estimates inside the pseudo-spectrum. We apply our results to the Kramers–Fokker–Planck operator.

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