Microlocal Analysis And Spectral Theory

Author : Luigi Rodino
Publisher : Springer Science & Business Media
Page : 449 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401156264

Get Book

Microlocal Analysis and Spectral Theory by Luigi Rodino Pdf

The NATO Advanced Study Institute "Microlocal Analysis and Spectral The ory" was held in Tuscany (Italy) at Castelvecchio Pascoli, in the district of Lucca, hosted by the international vacation center "11 Ciocco" , from September 23 to October 3, 1996. The Institute recorded the considerable progress realized recently in the field of Microlocal Analysis. In a broad sense, Microlocal Analysis is the modern version of the classical Fourier technique in solving partial differential equa tions, where now the localization proceeding takes place with respect to the dual variables too. Precisely, through the tools of pseudo-differential operators, wave-front sets and Fourier integral operators, the general theory of the lin ear partial differential equations is now reaching a mature form, in the frame of Schwartz distributions or other generalized functions. At the same time, Microlocal Analysis has grown up into a definite and independent part of Math ematical Analysis, with other applications all around Mathematics and Physics, one major theme being Spectral Theory for Schrodinger equation in Quantum Mechanics.

Author : Michael Demuth
Publisher : De Gruyter Akademie Forschung
Page : 376 pages
File Size : 40,5 Mb
Release : 1997
Category : Science
ISBN : UOM:39015048931508

Get Book

Spectral Theory, Microlocal Analysis, Singular Manifolds by Michael Demuth Pdf

Author : Victor Ivrii
Publisher : Springer Nature
Page : 739 pages
File Size : 55,8 Mb
Release : 2019-09-13
Category : Mathematics
ISBN : 9783030305611

Get Book

Microlocal Analysis, Sharp Spectral Asymptotics and Applications V by Victor Ivrii Pdf

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.

Author : Victor Ivrii
Publisher : Springer Nature
Page : 889 pages
File Size : 50,8 Mb
Release : 2019-09-12
Category : Mathematics
ISBN : 9783030305574

Get Book

Microlocal Analysis, Sharp Spectral Asymptotics and Applications I by Victor Ivrii Pdf

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.

Author : Victor Ivrii
Publisher : Springer Science & Business Media
Page : 736 pages
File Size : 44,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662124963

Get Book

Microlocal Analysis and Precise Spectral Asymptotics by Victor Ivrii Pdf

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.

Author : Victor Ivrii
Publisher : Springer Nature
Page : 729 pages
File Size : 41,7 Mb
Release : 2019-09-12
Category : Mathematics
ISBN : 9783030305376

Get Book

Microlocal Analysis, Sharp Spectral Asymptotics and Applications III by Victor Ivrii Pdf

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.

Author : Victor Ivrii
Publisher : Springer Nature
Page : 714 pages
File Size : 48,9 Mb
Release : 2019-09-11
Category : Mathematics
ISBN : 9783030305451

Get Book

Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV by Victor Ivrii Pdf

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.

Author : Daniel Grieser,Stefan Teufel,Andras Vasy
Publisher : Springer Science & Business Media
Page : 148 pages
File Size : 46,9 Mb
Release : 2012-12-13
Category : Mathematics
ISBN : 9783034804660

Get Book

Microlocal Methods in Mathematical Physics and Global Analysis by Daniel Grieser,Stefan Teufel,Andras Vasy Pdf

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.​

Author : Victor Ivrii
Publisher : Springer Nature
Page : 525 pages
File Size : 52,6 Mb
Release : 2019-09-11
Category : Mathematics
ISBN : 9783030305413

Get Book

Microlocal Analysis, Sharp Spectral Asymptotics and Applications II by Victor Ivrii Pdf

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.

Author : Marius Mantoiu,Georgi Raikov,Rafael Tiedra de Aldecoa
Publisher : Birkhäuser
Page : 255 pages
File Size : 42,5 Mb
Release : 2016-06-30
Category : Mathematics
ISBN : 9783319299921

Get Book

Spectral Theory and Mathematical Physics by Marius Mantoiu,Georgi Raikov,Rafael Tiedra de Aldecoa Pdf

The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schrödinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics. It will be of interest to researchers and graduate students in Mathematics and Mathematical Physics.

Author : Alain Grigis,Johannes Sjöstrand
Publisher : Cambridge University Press
Page : 164 pages
File Size : 55,6 Mb
Release : 1994-03-03
Category : Mathematics
ISBN : 0521449863

Get Book

Microlocal Analysis for Differential Operators by Alain Grigis,Johannes Sjöstrand Pdf

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

Author : Pablo Miranda,Nicolas Popoff,Georgi Raikov
Publisher : Springer Nature
Page : 272 pages
File Size : 42,7 Mb
Release : 2020-11-12
Category : Mathematics
ISBN : 9783030555566

Get Book

Spectral Theory and Mathematical Physics by Pablo Miranda,Nicolas Popoff,Georgi Raikov Pdf

This proceedings volume contains peer-reviewed, selected papers and surveys presented at the conference Spectral Theory and Mathematical Physics (STMP) 2018 which was held in Santiago, Chile, at the Pontifical Catholic University of Chile in December 2018. The original works gathered in this volume reveal the state of the art in the area and reflect the intense cooperation between young researchers in spectral theoryand mathematical physics and established specialists in this field. The list of topics covered includes: eigenvalues and resonances for quantum Hamiltonians; spectral shift function and quantum scattering; spectral properties of random operators; magnetic quantum Hamiltonians; microlocal analysis and its applications in mathematical physics. This volume can be of interest both to senior researchers and graduate students pursuing new research topics in Mathematical Physics.

Author : Victor Ivrii
Publisher : Unknown
Page : 128 pages
File Size : 43,6 Mb
Release : 2019
Category : Asymptotic expansions
ISBN : 3030305627

Get Book

Microlocal Analysis, Sharp Spectral Asymptotics and Applications by Victor Ivrii Pdf

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.

Author : M.A. Shubin
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 54,6 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9783642565793

Get Book

Pseudodifferential Operators and Spectral Theory by M.A. Shubin Pdf

I had mixed feelings when I thought how I should prepare the book for the second edition. It was clear to me that I had to correct all mistakes and misprints that were found in the book during the life of the first edition. This was easy to do because the mistakes were mostly minor and easy to correct, and the misprints were not many. It was more difficult to decide whether I should update the book (or at least its bibliography) somehow. I decided that it did not need much of an updating. The main value of any good mathematical book is that it teaches its reader some language and some skills. It can not exhaust any substantial topic no matter how hard the author tried. Pseudodifferential operators became a language and a tool of analysis of partial differential equations long ago. Therefore it is meaningless to try to exhaust this topic. Here is an easy proof. As of July 3, 2000, MathSciNet (the database of the American Mathematical Society) in a few seconds found 3695 sources, among them 363 books, during its search for "pseudodifferential operator". (The search also led to finding 963 sources for "pseudo-differential operator" but I was unable to check how much the results ofthese two searches intersected). This means that the corresponding words appear either in the title or in the review published in Mathematical Reviews.

Author : Michael Eugene Taylor
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 48,9 Mb
Release : 1984
Category : Differential equations, Hypoelliptic
ISBN : 9780821823149

Get Book

Noncommutative Microlocal Analysis by Michael Eugene Taylor Pdf