Decoding the Kramers–Fokker–Planck Operator: An Overview

This chapter provides a comprehensive survey of several articles, including (Ben Said et al., Asymptot. Anal. 119(1-2), 87–116 (2020); Ben Said, J. Inst. Math. Jussieu 21(2), 675–711 (2022); Ben Said, Math. Methods Appl. Sci. 45(2), 914–927 (2022)), that delve into the properties and compactness criteria for the resolvent of the Kramers–Fokker–Planck operator. By reviewing these works, we aim to gain insights into the fundamental aspects and analysis techniques associated with this operator.