Grushin Operator on Infinite Dimensional Homogeneous Lie Groups

2024/11/22 by Egwe, M. E., Opadara, J. I.
#22Exx #32W05 #47Axx #47Dxx #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2411.19697

Abstract

A collection of infinite dimensional complete vector fields \V_i\_i=1^∞ acting on a locally convex manifolds M on which a smooth positive measure μ is defined was considered. It was assumed that the vector fields generates an infinite dimensional Lie algebra \mathfrakg and satisfies Hormander's condition. The sum of squares of Grushin operators related to the vector fields was examined and the operator is then considered as the generalized Grushin operator. The paramount proofs were Poincar\acutee inequality, Gaussian two-bounded estimate for the related heat kernels and the doubling condition for the metric defined by the underlying vector fields.

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