Wave Kernels of the Twisted Laplacian

2007 ◽  
pp. 107-115 ◽  
Author(s):  
Jingzhi Tie ◽  
M. W. Wong
Keyword(s):  
Twisted Laplacian

scholarly journals Spectral projections for the twisted Laplacian

2007 ◽  
Vol 180 (2) ◽  
pp. 103-110 ◽  
Author(s):  
Herbert Koch ◽  
Fulvio Ricci
Keyword(s):  
Twisted Laplacian ◽  
Spectral Projections

The Schrödinger kernel of the twisted Laplacian and cyclic models

2010 ◽  
Vol 95 (6) ◽  
pp. 593-599 ◽  
Author(s):  
Shahla Molahajloo ◽  
M. W. Wong
Keyword(s):  
Twisted Laplacian ◽  
Cyclic Models

scholarly journals Global Gevrey hypoellipticity for the twisted Laplacian on forms

2017 ◽  
Vol 9 (2) ◽  
pp. 151-171
Author(s):  
Wei-Xi Li ◽  
Alberto Parmeggiani ◽  
Yan-Lin Wang
Keyword(s):  
Twisted Laplacian

scholarly journals On the Wave Equation Associated to the Hermite and the Twisted Laplacian

2009 ◽  
Vol 16 (2) ◽  
pp. 294-310 ◽  
Author(s):  
Piero D’Ancona ◽  
Vittoria Pierfelice ◽  
Fulvio Ricci
Keyword(s):  
Wave Equation ◽  
Twisted Laplacian

scholarly journals On Concrete Spectral Properties of a Twisted Laplacian Associated with a Central Extension of the Real Heisenberg Group

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Aymane El Fardi ◽  
Allal Ghanmi ◽  
Ahmed Intissar
Keyword(s):  
Heisenberg Group ◽  
Central Extension ◽  
Spectral Properties ◽  
The Real ◽  
Invariance Properties ◽  
Heisenberg Type ◽  
Twisted Laplacian

We consider the special magnetic Laplacian given byΔν,μ=4∑j=1n∂2/∂zj∂zj¯+2iνE+E¯+n+2μE-E¯-ν2+μ2z2. We show thatΔν,μis connected to the sub-Laplacian of a group of Heisenberg type given byC ×ω Cnrealized as a central extension of the real Heisenberg groupH2n+1. We also discuss invariance properties ofΔν,μand give some of their explicit spectral properties.

scholarly journals Multipliers for the twisted Laplacian

2003 ◽  
Vol 97 (2) ◽  
pp. 189-205
Author(s):  
E. K. Narayanan
Keyword(s):  
Twisted Laplacian

scholarly journals Hermite functions and special Hermite functions  depending on Heisenberg group (ℍⁿ ): دوال هرميت ودوال هرميت الخاصة اعتماداً على زمرة هايزنبرغ (ℍⁿ)

2020 ◽  
Vol 4 (2) ◽  
Author(s):  
Soha Ali Salamah
Keyword(s):  
Representation Theory ◽  
Harmonic Oscillator ◽  
Heisenberg Group ◽  
Hermite Functions ◽  
Hermite Operator ◽  
Twisted Laplacian ◽  
Special Hermite Functions ◽  
Hermite Operators ◽  
The Relationship ◽  
Hermite Expansions

In this paper, we talk about Heisenberg group, the most known example from the lie groups. After that, we talk about the representation theory of this group, and the relationship between the representation theory of the Heisenberg group and the position and momentum operator and momentum operators (ors). relationship between the representation theory of the Heisenberg group and the position and momentum, that shows how we will make the connection between the Heisenberg group and physics. Then we introduce and study some properties of the Hermite and special Hermite functions. These functions are eigenfunctions of the Hermite and special Hermite operators, respectively. The Hermite operator is often called the harmonic oscillator and the special Hermite operator is sometimes called the twisted Laplacian. As we will later see, the two operators are directly related to the sub-laplacian on the Heisenberg group. The theory of Hermite and special Hermite expansions is intimately connected to the harmonic analysis on the Heisenberg group. They play an important role in our understanding of several problems on ℍⁿ .

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