Intrinsic Taylor formula for non-homogeneous Kolmogorov-type Lie groups

2017/07/05 by Stefano Pagliarani, Pagliarani, Stefano, Michele Pignotti +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #advanced mathematical theories #math.AP

paper · pdf · doi:10.48550/arxiv.1707.01422

openalex publication_date 2017/07/05 · arxiv created 2017/07/06 · arxiv updated 2017/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an intrinsic Taylor-like formula for a class of Lie groups arising in the study of some sub-elliptic differential operators, namely the Kolmogorov operators. The estimate of the remainder is in terms of the intrinsic norm induced by such operators. These results extend the recent developments in a work by Pascucci and the present authors, where a full characterization of the intrinsic Hölder spaces and their Taylor polynomials were given under the additional assumption that the Lie group is homogeneous in the sense of Folland & Stein. Remarkably, the intrinsic Taylor polynomial admits the same representation as in the homogeneous case.

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