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《偏微分方程通讯》2013,38(3-4):745-769
Abstract We obtain an explicit representation formula for the sub-Laplacian on the isotropic, three-dimensional Heisenberg group. Using the formula we obtain themeromorphic continuation of the resolvent to the logarithmic plane, the existence of boundary values in the continuous spectrum, and semiclassical asymptotics of the resolvent kernel. The asymptotic formulas show the contribution of each Hamiltonian path in Carnot geometry to the spatial and high-energy asymptotics of the resolvent (convolution) kernel for the sub-Laplacian. 相似文献
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Riccardo Adami Ugo Boscain Valentina Franceschi Dario Prandi 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(4):1095-1113
In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on is essentially self-adjoint in . A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on is never essentially self-adjoint in , if . We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass. 相似文献
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We introduce the quaternion Heisenberg group and show that it is a special case of the model step two nilpotent Lie group
studied by Beals, Gaveau and Greiner. Using the heat kernel, we give formulas for Green functions of sub-Laplacians on the
quaternion Heisenberg group.
This research has been supported by the Natural Sciences and Engineering Research Council of Canada. 相似文献
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Emilie David-Guillou 《Journal of Functional Analysis》2006,238(2):734-750
We consider a family of real NA groups with rank two, and we prove that these groups have sub-Laplacians with differentiable Lp functional calculus for all p?1. 相似文献
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Der Chen CHANG Jing Zhi TIE 《数学学报(英文版)》2005,21(4):803-818
In this note, we compute the fundamental solution for the Hermite operator with singularity at an arbitrary point y∈R^n. We also apply this result to obtain the fundamental solutions for the Grushin operator in R^2 and the sub-Laplacian in the Heisenberg group Hn. 相似文献
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Jingzhi Tie 《偏微分方程通讯》2013,38(7):1047-1069