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The Heisenberg Group

2017
One of the big contributions of E. M. Stein is the development of harmonic analysis on the Heisenberg group. In a fundamental joint paper with G. B. Folland, Stein laid all the groundwork for this study. In this chapter we reproduce and develop some of that groundwork.
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Optimal Control on the Heisenberg Group

Journal of Dynamical and Control Systems, 1999
The paper studies an optimal control problem where the controlled dynamics is given by the conservation of the angular momentum and the cost functional is described by the total kinetic energy. A geometric analysis of minimizing curves is provided.
Monroy-Pérez, F., Anzaldo-Meneses, A.
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The Compactness of Commutators on the Heisenberg Group

Acta Mathematica Sinica, English Series, 2005
The Heisenberg group \(\mathbf{H}\) is a Lie group with underlying manifold \({\mathbb R}\times{\mathbb C}\). The group law is given by \[ t(t,z)(t',z')= (t+t'+2\operatorname{Im}z\overline{z'},z+z'). \] Let \(M(\lambda)\) be an operator-valued function such that \(\sup_{\lambda\in{\mathbb R}^*}\| M (\lambda)\| _{\text{op}}
Liu, Heping, Zheng, Xuanyuan
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The Heisenberg group

2001
Abstract The Heisenberg Group and its Fundamental Representation Associated with the symplectic phase space V is the Heisenberg group. This matrix group is defined over Z, and gives the extension of Heis to characteristic 2. We prefer to keep the symmetric form of Heis, which shows more clearly the symmetry between x and y, ‘position ...
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Magnetism in One-Dimensional Systems—The Heisenberg Model for Infinite Spin

American Journal of Physics, 1964
Michael E Fisher
exaly  

Rectifiability and perimeter in the Heisenberg group

Mathematische Annalen, 2001
Bruno Franchi   +2 more
exaly  

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