The Laguerre calculus on the nilpotent Lie groups of step two

2019/01/19 by Chang, Der-Chen, Markina, Irina, Wang, Wei
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.06513

Abstract

The Laguerre calculus is widely used for the inversion of differential operators on the Heisenberg group. We extend the Laguerre calculus for nilpotent groups of step two, and test it in the determining of the fundamental solution of the sub-Laplace operator. We also apply it to find the Szegö kernels of the projection operators to a kind of regular functions on the quaternion Heisenberg group.

Related

• Spectral projection operators of the Sub-Laplacian and Laguerre calculus on non-degenerate nilpotent Lie groups of step two
• Semiclassical functional calculus on nilpotent Lie groups and their compact nilmanifolds
• An integral representation for Folland's fundamental solution of the sub-Laplacian on Heisenberg groups ℍⁿ
• Intrinsic Lipschitz maps vs. Lagrangian type solutions in Carnot groups of step 2
• A heat kernel version of Miyachi's Theorem for the Laguerre hypergroup