Quaternionic structure and analysis of some Kramers–Fokker–Planck operators

Article type: Research Article

Authors: Said, Mona Ben^{a; *} | Nier, Francis^a | Viola, Joe^b

Affiliations: [a] Laboratoire Analyse, Géométrie et Applications, Université Paris 13, 99 Avenue Jean Baptiste Clément, 93430 Villetaneuse, France. E-mails: bensaid@univ-paris13.fr, nier@math.univ-paris13.fr | [b] Laboratoire de Mathématiques Jean Leray, Université de Nantes, 2, rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France. E-mail: Joseph.Viola@univ-nantes.fr

Correspondence: [*] Corresponding author. E-mail: bensaid@univ-paris13.fr.

Abstract: The present article is concerned with global subelliptic estimates for Kramers–Fokker–Planck operators with polynomials of degree less than or equal to two. The constants appearing in those estimates are accurately formulated in terms of the coefficients, especially when those are large.

Keywords: Subelliptic estimates, compact resolvent, Kramers–Fokker–Planck operator, quaternions, Bargmann transform

DOI: 10.3233/ASY-191569

Journal: Asymptotic Analysis, vol. 119, no. 1-2, pp. 87-116, 2020