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

TL;DR

This paper investigates subelliptic estimates for certain Kramers-Fokker-Planck operators with quadratic polynomial coefficients, providing precise formulations of the constants involved, especially for large coefficients.

Contribution

It introduces a detailed analysis of subelliptic estimates for Kramers-Fokker-Planck operators with quadratic polynomials, emphasizing explicit constant formulations.

Findings

Explicit constants for subelliptic estimates formulated

Analysis applicable to operators with large coefficients

Enhanced understanding of the operator's regularity properties

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.