Spectral properties of the Kramers-Fokker-Planck operator with a long-range potential

2024/06/07 by Wang, Xue Ping · 1 citation
#35J10 #35P15 #47A55 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2406.05206

Abstract

We study real resonances and embedded eigenvalues of the Kramers--Fokker--Planck operator with a long-range potential. We prove that thresholds are only possible accumulation points of eigenvalues and that the limiting absorption principle holds true for energies outside an exceptional set. We also prove that the eigenfunctions associated with discrete eigenvalues decay exponentially and those associated with embedded non-threshold ones decay polynomially.

Cited by

• The Kramers-Fokker-Planck equation with a decaying potential in \mathbb Rⁿ, n ≥ 4

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