Semiclassical analysis for the Kramers-Fokker-Planck equation

2004/06/14 by Frederic Herau, Frédéric Hérau, Johannes Sjoestrand +4
Mathematics · Physics and Astronomy · #35P20 #35S10 #47A10 #47D06 #Advanced Mathematical Physics Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:35P20 #msc:35S10 #msc:47A10 #msc:47D06

paper · pdf · doi:10.48550/arxiv.math/0406275

arxiv created 2004/06/14 · openalex publication_date 2004/06/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Isotropic Hypoellipticity and Trend to Equilibrium for the Fokker-Planck Equation with a High-Degree Potential

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