Geometry and Analysis of the Grusin Operator

Authors

• Gustavo Hoepfner, University of Arkansas, Fayetteville
• Andrew Raich, University of Arkansas, FayettevilleFollow

Document Type

Article

Publication Date

10-22-2025

Keywords

Grusin operator, Grusin resolvent, Grusin heat equation, Mehler's formula, Hermite functions, Grusin operator, Grusin resolvent, Grusin heat equation, Global L-1-Gevrey functions, Mehler's formula, Hermite functions

Abstract

In this paper we introduce a new technique for analyzing the heat kernel associated to the Grusin Laplacian. We prove pointwise estimates for arbitrary derivatives of the Grusin heat kernel and the resolvent in terms of the control distance associated with the Grusin operator. Our technique is based on the globalL(1)-Gevrey method.

Comments

Web of Science

Springer

Citation

Hoepfner, G., Raich, A. Geometry and Analysis of the Grusin Operator. J Geom Anal 35, 402 (2025). https://doi.org/10.1007/s12220-025-02236-5

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.