Intrinsic Taylor formula for Kolmogorov-type homogeneous groups

TL;DR

This paper develops an intrinsic Taylor formula for a class of Kolmogorov-type operators, providing bounds for the remainder in terms of the associated homogeneous Lie group norm, advancing the understanding of these operators.

Contribution

It introduces an intrinsic Taylor expansion with global and local bounds tailored to Kolmogorov-type operators within homogeneous Lie groups.

Findings

Established an intrinsic Taylor formula for Kolmogorov operators

Provided bounds for the Taylor remainder in the homogeneous Lie group norm

Enhanced analytical tools for ultra-parabolic differential operators

Abstract

We consider a class of ultra-parabolic Kolmogorov-type operators satisfying the Hormander's condition. We prove an intrinsic Taylor formula with global and local bounds for the remainder given in terms of the norm in the homogeneous Lie group naturally associated to the differential operator.