Microlocal Analysis for Differential Operators

An Introduction

Author: Alain Grigis,Johannes Sjöstrand

Publisher: Cambridge University Press

ISBN: 9780521449861

Category: Mathematics

Page: 151

View: 4814

This book corresponds to a graduate course given many times by the authors, and should prove to be useful to mathematicians and theoretical physicists.
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Geometric Analysis

Author: Hubert L. Bray,Greg Galloway,Rafe Mazzeo,Natasa Sesum

Publisher: American Mathematical Soc.

ISBN: 1470423138

Category: Geometric analysis

Page: 456

View: 1118

This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace–Beltrami operators.
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Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators

Author: Nicolas Lerner

Publisher: Springer Science & Business Media

ISBN: 9783764385101

Category: Mathematics

Page: 397

View: 5360

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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Nonlinear Optical and Atomic Systems

At the Interface of Physics and Mathematics

Author: Christophe Besse,Jean-Claude Garreau

Publisher: Springer

ISBN: 3319190156

Category: Science

Page: 338

View: 8340

Focusing on the interface between mathematics and physics, this book offers an introduction to the physics, the mathematics, and the numerical simulation of nonlinear systems in optics and atomic physics. The text covers a wide spectrum of current research on the subject, which is an extremely active field in physics and mathematical physics, with a very broad range of implications, both for fundamental science and technological applications: light propagation in microstructured optical fibers, Bose-Einstein condensates, disordered systems, and the newly emerging field of nonlinear quantum mechanics. Accessible to PhD students, this book will also be of interest to post-doctoral researchers and seasoned academics.
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Eigenfunctions of the Laplacian on a Riemannian Manifold

Author: Steve Zelditch

Publisher: American Mathematical Soc.

ISBN: 1470410370

Category: Eigenfunctions

Page: 394

View: 4967

Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.
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Mathematical Models, Methods and Applications

Author: Abul Hasan Siddiqi,Pammy Manchanda,Rashmi Bhardwaj

Publisher: Springer

ISBN: 9812879730

Category: Mathematics

Page: 298

View: 5715

The present volume contains invited talks of 11th biennial conference on “Emerging Mathematical Methods, Models and Algorithms for Science and Technology”. The main message of the book is that mathematics has a great potential to analyse and understand the challenging problems of nanotechnology, biotechnology, medical science, oil industry and financial technology. The book highlights all the features and main theme discussed in the conference. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world.
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Evolution equations

existence, regularity and singularities

Author: Bogdan Bojarski,Dariusz Wrzosek,Wojciech M. Zajączkowski,Stefan Banach International Mathematical Center

Publisher: N.A

ISBN: N.A

Category: Evolution equations

Page: 226

View: 4944

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Asymptotic Analysis in General Relativity

Author: Thierry Daudé,Dietrich Häfner,Jean-Philippe Nicolas

Publisher: Cambridge University Press

ISBN: 1316649407

Category: Mathematics

Page: N.A

View: 6266

Introduction to modern methods for classical and quantum fields in general relativity / Thierry Daudé, Dietrich Häfner, and Jean-Philippe Nicolas -- Geometry of black hole spacetimes / Lars Andersson, Thomas B. Ackdahl, and Pieter Blue -- An introduction to Quantum Field Theory on curved space-times / Christian Gerard -- A minicourse on microlocal analysis for wave propagation / Andras Vasy -- An introduction to conformal geometry and tractor calculus, with a view to applications in general relativity / Sean N. Curry and A. Rod Gover
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Lectures on the Ricci Flow

Author: Peter Topping

Publisher: Cambridge University Press

ISBN: 0521689473

Category: Mathematics

Page: 113

View: 9206

An introduction to Ricci flow suitable for graduate students and research mathematicians.
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Encyclopedia of mathematical physics

Author: Sheung Tsun Tsou

Publisher: Academic Pr

ISBN: 9780125126601

Category: Science

Page: 3500

View: 1082

The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originated from work in mathematical physics by providing them with focused high quality background information. * First comprehensive interdisciplinary coverage * Mathematical Physics explained to stimulate new developments and foster new applications of its methods to other fields * Written by an international group of experts * Contains several undergraduate-level introductory articles to facilitate acquisition of new expertise * Thematic index and extensive cross-referencing to provide easy access and quick search functionality * Also available online with active linking.
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Mathematik und Technologie

Author: Christiane Rousseau,Yvan Saint-Aubin

Publisher: Springer-Verlag

ISBN: 3642300928

Category: Mathematics

Page: 609

View: 690

Zusammen mit der Abstraktion ist die Mathematik das entscheidende Werkzeug für technologische Innovationen. Das Buch bietet eine Einführung in zahlreiche Anwendungen der Mathematik auf dem Gebiet der Technologie. Meist werden moderne Anwendungen dargestellt, die heute zum Alltag gehören. Die mathematischen Grundlagen für technologische Anwendungen sind dabei relativ elementar, was die Leistungsstärke der mathematischen Modellbildung und der mathematischen Hilfsmittel beweist. Mit zahlreichen originellen Übungen am Ende eines jeden Kapitels.
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