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Quantization on Nilpotent Lie Groups
Preface.- Introduction.- Notation and conventions.- 1 Preliminaries on Lie groups.- 2 Quantization on compact Lie groups.- 3 Homogeneous Lie groups.- 4 Rockland operators and Sobolev spaces.- 5
Pseudo-differential operators on the Heisenberg group
The Heisenberg group was introduced in Example 1.6.4. It was our primal example of a stratified Lie group, see Section 3.1.1. Due to the importance of the Heisenberg group and of its many
Sobolev spaces on graded lie groups
— In this article, we study the Lp-properties of powers of positive Rockland operators and define Sobolev spaces on general graded Lie groups. We establish that the defined Sobolev spaces are
A Pseudo-differential Calculus on Graded Nilpotent Lie Groups
In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using
Gelfand transforms of SO(3)-invariant Schwartz functions on the free group N_{3,2}
The spectrum of a Gelfand pair $(K\ltimes N, K)$, where $N$ is a nilpotent group, can be embedded in a Euclidean space. We prove that in general, the Schwartz functions on the spectrum are the
Heisenberg-Modulation Spaces at the Crossroads of Coorbit Theory and Decomposition Space Theory.
We show that generalised time-frequency shifts on the Heisenberg group $\mathbf{H}_n \cong \mathbb{R}^{2n+1}$, realised as a unitary irreducible representation of a nilpotent Lie group acting on
The Heisenberg oscillator
In this short note, we determine the spectrum of the Heisenberg oscillator which is the operator defined as $$L+|x|^2+|y|^2$$ on the Heisenberg group $$H_1=\mathbb{ R} ^2_{x,y}\times \mathbb{ R} $$
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