Microlocal Analysis Sharp Spectral Asymptotics And Applications Iv
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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 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 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 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.
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.
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.
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 Iv
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Author : Victor Ivrii
language : en
Publisher:
Release Date : 2019
Microlocal Analysis Sharp Spectral Asymptotics And Applications Iv 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 Analysis (Mathematics). categories.
Recent Advances In Operator Theory Operator Algebras And Their Applications
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Author : Dumitru Gaspar
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Recent Advances In Operator Theory Operator Algebras And Their Applications written by Dumitru Gaspar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.
This book offers peer-reviewed articles from the 19th International Conference on Operator Theory, Summer 2002. It contains recent developments in a broad range of topics from operator theory, operator algebras and their applications, particularly to differential analysis, complex functions, ergodic theory, mathematical physics, matrix analysis, and systems theory. The book covers a large variety of topics including single operator theory, C*-algebras, diffrential operators, integral transforms, stochastic processes and operators, and more.
Microlocal Analysis And Precise Spectral Asymptotics
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Author : Victor Ivrii
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Microlocal Analysis And Precise Spectral Asymptotics written by Victor Ivrii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
The problem of spectral asymptotics, in particular the problem of the asymptotic dis tribution of eigenvalues, is one of the central problems in the spectral theory of partial differential operators; moreover, it is very important for the general theory of partial differential operators. I started working in this domain in 1979 after R. Seeley found a remainder estimate of the same order as the then hypothetical second term for the Laplacian in domains with boundary, and M. Shubin and B. M. Levitan suggested that I should try to prove Weyl's conjecture. During the past fifteen years I have not left the topic, although I had such intentions in 1985 when the methods I invented seemed to fai! to provide furt her progress and only a couple of not very exciting problems remained to be solved. However, at that time I made the step toward local semiclassical spectral asymptotics and rescaling, and new horizons opened.