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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.- 5Expand
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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 manyExpand
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Lower bounds for operators on graded Lie groups
Abstract In this note we present a symbolic pseudo-differential calculus on any graded (nilpotent) Lie group and, as an application, a version of the sharp Garding inequality. As a corollary, weExpand
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Semi-classical analysis on H-type groups
In this paper, we develop semi-classical analysis on H-type groups. We define semi-classical pseudodi fferential operators, prove the boundedness of their action on square integrable functions andExpand
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Intrinsic pseudo-differential calculi on any compact Lie group
Abstract In this paper, we define in an intrinsic way operators on a compact Lie group by means of symbols using the representations of the group. The main purpose is to show that these operatorsExpand
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The bounded spherical functions for the free two step nilpotent Lie group
In this paper, we give the expressions for the bounded spherical functions, or equivalently the spherical functions of positive type, for the free two-step nilpotent Lie groups endowed with theExpand
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A pseudo-differential calculus on the Heisenberg group
In this note we present a symbolic pseudo-differential calculus on the Heisenberg group. We particularise to this group our general construction [4,2,3] of pseudo-differential calculi on gradedExpand
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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 areExpand
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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 $$H_1=\mathbb{ R} ^2_{x,y}\times \mathbb{ R} $$Expand
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Differential structure on the dual of a compact lie group
In this paper we define difference operators and homogeneous Sobolev-type spaces on the dual of a compact Lie group. As an application and to show that this defines a relevant differential structure,Expand
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