Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators [recurso electrónico] / by Nicolas Lerner.

Por: Lerner, Nicolas [author.]Colaborador(es): SpringerLink (Online service)Tipo de material: TextoTextoSeries Pseudo-Differential Operators, Theory and Applications ; 3Editor: Basel : Birkhäuser Basel, 2010Descripción: xii, 397 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783764385101Tema(s): Mathematics | Global analysis (Mathematics) | Mathematics | AnalysisFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 515 Clasificación LoC:QA299.6-433Recursos en línea: Libro electrónicoTexto
Contenidos:
Basic Notions of Phase Space Analysis -- Metrics on the Phase Space -- Estimates for Non-Selfadjoint Operators.
En: Springer eBooksResumen: 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.
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Basic Notions of Phase Space Analysis -- Metrics on the Phase Space -- Estimates for Non-Selfadjoint Operators.

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.

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