V´Eronique Fischer
Abstract. We discuss the recent developments of semi-classical and micro-local analysis in the context of nilpotent Lie groups and for sub-elliptic operators. In particular, we give an overview of pseudo-differential calculi recently defined on nilpotent Lie groups as well as of the notion of quantum limits in the Euclidean and nilpotent cases.
2010 Msc. 43A80; 58J45, 35Q40.
Keywords. Analysis on nilpotent Lie groups, evolution of solutions to the Schr¨odinger equation, micro-local and semi-classical analysis for sub-elliptic operators, abstract harmonic analysis, C∗- algebra theory.
Contents
1.
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1.1. The questions in the elliptic framework.
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1.2. Sub-elliptic operators.
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1.3.
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1.4.
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2.
4
2.1.
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2.2.
5
2.3.
6
2.4.
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3. Pseudo-differential theory and quantum limits on nilpotent Lie groups
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3.1.
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3.2. Pseudo-differential calculi on graded nilpotent Lie groups
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3.3.
11
3.4.
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3.5.
12
3.6.
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