Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds

Raphael S. Pongee

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Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds

机译：海森堡流形上的海森堡微积分和次椭圆算子的谱理论

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This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner and Taylor.

机译：该回忆录涉及海森堡流形上的次椭圆演算，包括CR和接触流形。在这种情况下，主要的差分算子包括Hormander平方和，Kohn Laplacian，水平次拉普拉斯算子，Gover-Graham的CR共形算子和接触Laplacian。这些算子不能是椭圆形的，而Beals-Greiner和Taylor的Heisenberg微积分提供了研究它们的相关伪微积分。

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《Memoirs of the American Mathematical Society》 |2008年第906期|共134页
作者
Raphael S. Pongee;
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正文语种 eng
中图分类数学;
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Heisenberg calculus; complex powers; heat equation; spectral asymptotics; analysis on CR and contact manifolds; hypoelliptic operators;

机译：海森堡演算;复幂;热方程;谱渐近;CR和接触流形分析;降椭圆算子;

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1. Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds [J] . Raphael S. Pongee Memoirs of the American Mathematical Society . 2008,第906期

机译：海森堡流形上的海森堡微积分和次椭圆算子的谱理论
2. ISOSPECTRAL DEFORMATIONS ON RIEMANNIAN MANIFOLDS WHICH ARE DIFFEOMORPHIC TO COMPACT HEISENBERG MANIFOLDS [J] . Schueth D. Commentarii Mathematici Helvetici . 1995,第3期

机译：紧凑型海森堡流形的RIEMANNIAN流形的等离子变形
3. Perturbation theory for Heisenberg operators - art. no. 022104 [J] . Fernandez FM. Physical Review, A. Atomic, molecular, and optical physics . 2003,第2期

机译：海森堡算子的摄动理论-艺术。没有。 022104
4. Spectral theory of the Schrodinger operators on non-compact manifolds: qualitative results [C] . Mikhail Shubin ICMS Instructional Conference . 1999

机译：非紧致歧管的Schrodinger运算符的光谱理论：定性结果
5. Geometric mapping theory of the Heisenberg group, sub-Riemannian manifolds, and hyperbolic spaces [D] . Lukyanenko, Anton 2014

机译：海森堡群，次黎曼流形和双曲空间的几何映射理论
6. Heat kernel asymptotic expansions for the Heisenberg sub-Laplacian and the Grushin operator [O] . Der-Chen Chang, Yutian Li -1

机译：Heisenberg次拉普拉斯算子和Grushin算子的热核渐近展开
7. Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds [O] . Ponge, Raphael 2005

机译：Heisenberg微积分和低周期算子的谱理论海森堡的流形
8. Spectral Estimates for the Magnetic Schoedinger Operator and the Heisenberg Laplacian [R] . Hansson, A. 2008

机译：磁学schededinger算子和Heisenberg拉普拉斯算子的谱估计

Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds

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