Microlocal Analysis, Sharp Spectral Asymptotics and Applications V
Title | Microlocal Analysis, Sharp Spectral Asymptotics and Applications V PDF eBook |
Author | Victor Ivrii |
Publisher | Springer Nature |
Pages | 739 |
Release | 2019-09-13 |
Genre | Mathematics |
ISBN | 3030305619 |
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
Title | Microlocal Analysis, Sharp Spectral Asymptotics and Applications I PDF eBook |
Author | Victor Ivrii |
Publisher | Springer Nature |
Pages | 889 |
Release | 2019-09-12 |
Genre | Mathematics |
ISBN | 3030305570 |
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
Title | Microlocal Analysis, Sharp Spectral Asymptotics and Applications PDF eBook |
Author | Victor Ivrii |
Publisher | |
Pages | |
Release | 2019 |
Genre | Asymptotic expansions |
ISBN | 9783030305628 |
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
Title | Microlocal Analysis, Sharp Spectral Asymptotics and Applications III PDF eBook |
Author | Victor Ivrii |
Publisher | Springer |
Pages | 0 |
Release | 2019-09-25 |
Genre | Mathematics |
ISBN | 9783030305369 |
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 IV
Title | Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV PDF eBook |
Author | Victor Ivrii |
Publisher | |
Pages | 0 |
Release | 2019 |
Genre | Analysis (Mathematics). |
ISBN | 9783030305468 |
Microlocal Analysis and Precise Spectral Asymptotics
Title | Microlocal Analysis and Precise Spectral Asymptotics PDF eBook |
Author | Victor Ivrii |
Publisher | Springer Science & Business Media |
Pages | 756 |
Release | 1998-05-20 |
Genre | Mathematics |
ISBN | 9783540627807 |
This long awaited book is devoted to the methods of microlocal semiclassical analysis in application to spectral asymptotics with accurate remainder estimates. The very powerful machinery of local and microlocal semiclassical spectral asymptotics is developed as well as methods in combining these asymptotics with spectral estimates. The rescaling technique should be mentioned as an easy as to use and very powerful tool. Many theorems, considered before as independent and difficult, now are just special cases of easy corollaries of the theorems proved in the book. Most of the results and almost all the proofs are as yet unpublished
Microlocal Analysis, Sharp Spectral Asymptotics and Applications III
Title | Microlocal Analysis, Sharp Spectral Asymptotics and Applications III PDF eBook |
Author | Victor Ivrii |
Publisher | Springer Nature |
Pages | 729 |
Release | 2019-09-12 |
Genre | Mathematics |
ISBN | 3030305376 |
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.