Microlocal Analysis Sharp Spectral Asymptotics And Applications V
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Microlocal Analysis Sharp Spectral Asymptotics And Applications V
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Author : Victor Ivrii
language : en
Publisher: Springer Nature
Release Date : 2019-09-13
Microlocal Analysis Sharp Spectral Asymptotics And Applications V written by Victor Ivrii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-13 with Mathematics categories.
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
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Author : Victor Ivrii
language : en
Publisher:
Release Date : 2019
Microlocal Analysis Sharp Spectral Asymptotics And Applications written by Victor Ivrii and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Asymptotic expansions categories.
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 Iii
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Author : Victor Ivrii
language : en
Publisher: Springer Nature
Release Date : 2019-09-12
Microlocal Analysis Sharp Spectral Asymptotics And Applications Iii written by Victor Ivrii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-12 with Mathematics categories.
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 Sharp Spectral Asymptotics And Applications I
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Author : Victor Ivrii
language : en
Publisher: Springer Nature
Release Date : 2019-09-12
Microlocal Analysis Sharp Spectral Asymptotics And Applications I written by Victor Ivrii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-12 with Mathematics categories.
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.
Microlocal Analysis Sharp Spectral Asymptotics And Applications Iv
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Author : Victor Ivrii
language : en
Publisher: Springer Nature
Release Date : 2019-09-11
Microlocal Analysis Sharp Spectral Asymptotics And Applications Iv written by Victor Ivrii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-11 with Mathematics categories.
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 Ii
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Author : Victor Ivrii
language : en
Publisher: Springer Nature
Release Date : 2019-09-11
Microlocal Analysis Sharp Spectral Asymptotics And Applications Ii written by Victor Ivrii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-11 with Mathematics categories.
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.
Schr Dinger Operators Eigenvalues And Lieb Thirring Inequalities
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Author : Rupert L. Frank
language : en
Publisher: Cambridge University Press
Release Date : 2022-11-17
Schr Dinger Operators Eigenvalues And Lieb Thirring Inequalities written by Rupert L. Frank and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-17 with Mathematics categories.
The analysis of eigenvalues of Laplace and Schrödinger operators is an important and classical topic in mathematical physics with many applications. This book presents a thorough introduction to the area, suitable for masters and graduate students, and includes an ample amount of background material on the spectral theory of linear operators in Hilbert spaces and on Sobolev space theory. Of particular interest is a family of inequalities by Lieb and Thirring on eigenvalues of Schrödinger operators, which they used in their proof of stability of matter. The final part of this book is devoted to the active research on sharp constants in these inequalities and contains state-of-the-art results, serving as a reference for experts and as a starting point for further research.
Differential Equations On Manifolds And Mathematical Physics
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Author : Vladimir M. Manuilov
language : en
Publisher: Springer Nature
Release Date : 2022-01-21
Differential Equations On Manifolds And Mathematical Physics written by Vladimir M. Manuilov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-21 with Mathematics categories.
This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries. The conference was mainly dedicated to partial differential equations on manifolds and their applications in mathematical physics, geometry, topology, and complex analysis. The volume contains selected contributions by leading experts in these fields and presents the current state of the art in several areas of PDE. It will be of interest to researchers and graduate students specializing in partial differential equations, mathematical physics, topology, geometry, and their applications. The readers will benefit from the interplay between these various areas of mathematics.
Functional Analytic Methods For Heat Green Operators
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Author : Kazuaki Taira
language : en
Publisher: Springer Nature
Release Date : 2024-09-18
Functional Analytic Methods For Heat Green Operators written by Kazuaki Taira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-18 with Mathematics categories.
This monograph guides the reader to the mathematical crossroads of heat equations and differential geometry via functional analysis. Following the recent trend towards constructive methods in the theory of partial differential equations, it makes extensive use of the ideas and techniques from the Weyl–Hörmander calculus of pseudo-differential operators to study heat Green operators through concrete calculations for the Dirichlet, Neumann, regular Robin and hypoelliptic Robin boundary conditions. Further, it provides detailed coverage of important examples and applications in elliptic and parabolic problems, illustrated with many figures and tables. A unified mathematical treatment for solving initial boundary value problems for the heat equation under general Robin boundary conditions is desirable, and leads to an extensive study of various aspects of elliptic and parabolic partial differential equations. The principal ideas are explicitly presented so that a broad spectrum of readers can easily understand the problem and the main results. The book will be of interest to readers looking for a functional analytic introduction to the meeting point of partial differential equations, differential geometry and probability.
Geometric Methods In Physics
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Author : Piotr Kielanowski
language : en
Publisher: Springer
Release Date : 2014-08-19
Geometric Methods In Physics written by Piotr Kielanowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-19 with Mathematics categories.
The Białowieża Workshops on Geometric Methods in Physics, which are hosted in the unique setting of the Białowieża natural forest in Poland, are among the most important meetings in the field. Every year some 80 to 100 participants from both the mathematics and physics world join to discuss new developments and to exchange ideas. The current volume was produced on the occasion of the 32nd meeting in 2013. It is now becoming a tradition that the Workshop is followed by a School on Geometry and Physics, which consists of advanced lectures for graduate students and young researchers. Selected speakers at the 2013 Workshop were asked to contribute to this book, and their work was supplemented by additional review articles. The selection shows that, despite its now long tradition, the workshop remains at the cutting edge of research. The 2013 Workshop also celebrated the 75th birthday of Daniel Sternheimer, and on this occasion the discussion mainly focused on his contributions to mathematical physics such as deformation quantization, Poisson geometry, symplectic geometry and non-commutative differential geometry.