Metrics on the phase space and non-selfadjoint pseudo-differential operators / by Nicolas Lerner
- 作者： Lerner, Nicolas.
- 其他作者：
- 其他題名：
- Springer eBooks
- 出版： Basel : Birkhauser Basel 2010
- 叢書名： Pseudo-differential operators, theory and applications ;v.3
- 主題： Pseudodifferential operators. , Nonselfadjoint operators. , Metric spaces. , Mathematics. , Analysis.
- ISBN： 9783764385101 (electronic bk.) 、 9783764385095 (paper)
- URL：
電子書
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讀者標籤：
- 系統號： 005178087 | 機讀編目格式
館藏資訊
This book is devoted to the study of pseudo-di?erential operators, with special emphasis on non-selfadjoint operators, a priori estimates and localization in the phase space. We have tried here to expose the most recent developments of the theory with its applications to local solvability and semi-classical estimates for non-selfadjoint operators. The?rstchapter,Basic Notions of Phase Space Analysis,isintroductoryand gives a presentation of very classical classes of pseudo-di?erential operators, along with some basic properties. As an illustration of the power of these methods, we give a proof of propagation of singularities for real-principal type operators (using aprioriestimates,andnotFourierintegraloperators),andweintroducethereader to local solvability problems. That chapter should be useful for a reader, say at the graduate level in analysis, eager to learn some basics on pseudo-di?erential operators. The second chapter, Metrics on the Phase Space begins with a review of symplectic algebra, Wigner functions, quantization formulas, metaplectic group and is intended to set the basic study of the phase space. We move forward to the more general setting of metrics on the phase space, following essentially the basic assumptions of L. H ̈ ormander (Chapter 18 in the book [73]) on this topic.