Microlocal Methods in Mathematical Physics and Global Analysis
Microlocal Methods in Mathematical Physics and Global Analysis

Author: Daniel Grieser

Publisher: Springer Science & Business Media

Published: 2012-12-13

Total Pages: 147

ISBN-13: 3034804660

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Microlocal analysis is a field of mathematics that was invented in the mid-20th century for the detailed investigation of problems from partial differential equations, which incorporated and made rigorous many ideas that originated in physics. Since then it has grown to a powerful machine which is used in global analysis, spectral theory, mathematical physics and other fields, and its further development is a lively area of current mathematical research. In this book extended abstracts of the conference 'Microlocal Methods in Mathematical Physics and Global Analysis', which was held at the University of Tübingen from the 14th to the 18th of June 2011, are collected.​

Microlocal Analysis, Sharp Spectral Asymptotics and Applications V
Microlocal Analysis, Sharp Spectral Asymptotics and Applications V

Author: Victor Ivrii

Publisher: Springer Nature

Published: 2019-09-13

Total Pages: 739

ISBN-13: 3030305619

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The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the methods developed in Volumes I, II, III and IV are applied to multiparticle quantum theory (asymptotics of the ground state energy and related problems), and to miscellaneous spectral problems.

Microlocal Analysis, Sharp Spectral Asymptotics and Applications I
Microlocal Analysis, Sharp Spectral Asymptotics and Applications I

Author: Victor Ivrii

Publisher: Springer Nature

Published: 2019-09-12

Total Pages: 889

ISBN-13: 3030305570

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The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the general microlocal semiclassical approach is developed, and microlocal and local semiclassical spectral asymptotics are derived.

New Trends in Microlocal Analysis
New Trends in Microlocal Analysis

Author: J.-M. Bony

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 237

ISBN-13: 4431684131

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Microlocal analysis began around 1970 when Mikio Sato, along with coauthors Masaki Kashiwara and Takahiro Kawai, wrote a decisive article on the structure of pseudodifferential equations, thus laying the foundation of D-modules and the singular spectrums of hyperfunctions. The key idea is the analysis of problems on the phase space, i.e., the cotangent bundle of the base space. Microlocal analysis is an active area of mathematical research that has been applied to many fields such as real and complex analysis, representation theory, topology, number theory, and mathematical physics. This volume contains the presentations given at a seminar jointly organized by the Japan Society for the Promotion of Science and Centre National des Recherches Scientifiques entitled New Trends in Microlocal Analysis. The book is divided into three parts: partial differential equations and mathematical analysis, mathematical physics, and algebraic analysis - D-modules and sheave theory. The large variety of new research that is covered will prove invaluable to students and researchers alike.

Microlocal Analysis, Sharp Spectral Asymptotics and Applications II
Microlocal Analysis, Sharp Spectral Asymptotics and Applications II

Author: Victor Ivrii

Publisher: Springer Nature

Published: 2019-09-11

Total Pages: 525

ISBN-13: 3030305414

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The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the local spectral asymptotics of Volume I in the regular part of the domain are combined with variational estimates in the vicinity of singularities, and global asymptotics are derived in the general form. They are then applied to multiple cases and asymptotics with respect to a spectral parameter. Finally, cases in which only general methods but not the results can be applied (non-standard asymptotics) are studied.

Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV
Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV

Author: Victor Ivrii

Publisher: Springer Nature

Published: 2019-09-11

Total Pages: 714

ISBN-13: 3030305457

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The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the methods developed in Volumes I, II and III are applied to the Schrödinger and Dirac operators in non-smooth settings and in higher dimensions.

Microlocal Analysis, Sharp Spectral Asymptotics and Applications III
Microlocal Analysis, Sharp Spectral Asymptotics and Applications III

Author: Victor Ivrii

Publisher: Springer Nature

Published: 2019-09-12

Total Pages: 729

ISBN-13: 3030305376

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The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the methods developed in Volumes I and II are applied to the Schrödinger and Dirac operators in smooth settings in dimensions 2 and 3.

Microlocal Analysis for Differential Operators
Microlocal Analysis for Differential Operators

Author: Alain Grigis

Publisher: Cambridge University Press

Published: 1994-03-03

Total Pages: 164

ISBN-13: 9780521449861

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

Microlocal Analysis and Inverse Problems in Tomography and Geometry
Microlocal Analysis and Inverse Problems in Tomography and Geometry

Author: Eric Todd Quinto

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2024-09-23

Total Pages: 252

ISBN-13: 3111338010

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Microlocal Analysis has proven to be a powerful tool for analyzing and solving inverse problems; including answering questions about stability, uniqueness, recovery of singularities, etc. This volume, presents several studies on microlocal methods in problems in tomography, integral geometry, geodesic transforms, travel time tomography, thermoacoustic tomography, Compton CT, cosmology, nonlinear inverse problems, and others.