Ivrii, Victor 1949
Overview
Works:  6 works in 40 publications in 3 languages and 800 library holdings 

Roles:  Author, Other 
Classifications:  QA3, 515.7242 
Publication Timeline
.
Most widely held works by
Victor Ivrii
The precise spectral asymptotics for elliptic operators acting in fiberings over manifolds with boundary by
Victor Ivrii(
Book
)
21 editions published in 1984 in English and Undetermined and held by 366 WorldCat member libraries worldwide
21 editions published in 1984 in English and Undetermined and held by 366 WorldCat member libraries worldwide
Microlocal analysis and precise spectral asymptotics by
Victor Ivrii(
Book
)
13 editions published between 1998 and 2011 in English and German and held by 222 WorldCat member libraries worldwide
Devoted to the methods of microlocal analysis applied to spectral asymptotics with accurate remainder estimates, this long awaited book develops the very powerful machinery of local and microlocal semiclassical spectral asymptotics, as well as methods of combining these asymptotics with spectral estimates. The rescaling technique, an easy to use and very powerful tool, is presented. Many theorems, considered till now as independent and difficult, are now just special cases of easy corollaries of the theorems proved in this book. Most of the results and their proofs are as yet unpublished. Part 1 considers semiclassical microlocal analysis and propagation of singularities inside the domain and near the boundary. Part 2 is on local and microlocal semiclassical spectral asymptotics for general operators and Schrödinger and Dirac operators. After a synthesis in Part 3, the real fun begins in Part 4: the main theorems are applied and numerous results, both known and new, are recovered with little effort. Then, in Chapter 12, nonWeyl asymptotics are obtained for operators in domains with thick cusps, degenerate operators, for spectral Riesz means for operators with singularities. Most of the results and almost all the proofs were never published
13 editions published between 1998 and 2011 in English and German and held by 222 WorldCat member libraries worldwide
Devoted to the methods of microlocal analysis applied to spectral asymptotics with accurate remainder estimates, this long awaited book develops the very powerful machinery of local and microlocal semiclassical spectral asymptotics, as well as methods of combining these asymptotics with spectral estimates. The rescaling technique, an easy to use and very powerful tool, is presented. Many theorems, considered till now as independent and difficult, are now just special cases of easy corollaries of the theorems proved in this book. Most of the results and their proofs are as yet unpublished. Part 1 considers semiclassical microlocal analysis and propagation of singularities inside the domain and near the boundary. Part 2 is on local and microlocal semiclassical spectral asymptotics for general operators and Schrödinger and Dirac operators. After a synthesis in Part 3, the real fun begins in Part 4: the main theorems are applied and numerous results, both known and new, are recovered with little effort. Then, in Chapter 12, nonWeyl asymptotics are obtained for operators in domains with thick cusps, degenerate operators, for spectral Riesz means for operators with singularities. Most of the results and almost all the proofs were never published
Partial differential equations IV : microlocal analysis and hyperbolic equations by
I︠U︡. V Egorov(
Book
)
2 editions published between 1993 and 2011 in English and held by 4 WorldCat member libraries worldwide
In the first part of this EMS volume Yu. V. Egorov gives an account of microlocal analysis as a tool for investigating partial differential equations. This method has become increasingly important in the theory of Hamiltonian systems. Egorov discusses the evolution of singularities of a partial differential equation and covers topics like integral curves of Hamiltonian systems, pseudodifferential equations and canonical transformations, subelliptic operators and Poisson brackets. The second survey written by V. Ya. Ivrii treats linear hyperbolic equations and systems. The author states necessary and sufficient conditions for C? and L2 wellposedness and he studies the analogous problem in the context of Gevrey classes. He also gives the latest results in the theory of mixed problems for hyperbolic operators and a list of unsolved problems. Both parts cover recent research in an important field, which before was scattered in numerous journals. The book will hence be of immense value to graduate students and researchers in partial differential equations and theoretical physics
2 editions published between 1993 and 2011 in English and held by 4 WorldCat member libraries worldwide
In the first part of this EMS volume Yu. V. Egorov gives an account of microlocal analysis as a tool for investigating partial differential equations. This method has become increasingly important in the theory of Hamiltonian systems. Egorov discusses the evolution of singularities of a partial differential equation and covers topics like integral curves of Hamiltonian systems, pseudodifferential equations and canonical transformations, subelliptic operators and Poisson brackets. The second survey written by V. Ya. Ivrii treats linear hyperbolic equations and systems. The author states necessary and sufficient conditions for C? and L2 wellposedness and he studies the analogous problem in the context of Gevrey classes. He also gives the latest results in the theory of mixed problems for hyperbolic operators and a list of unsolved problems. Both parts cover recent research in an important field, which before was scattered in numerous journals. The book will hence be of immense value to graduate students and researchers in partial differential equations and theoretical physics
Partial differential equations : [lectures given at the 1995 Annual Seminar of the Canadian Mathematical Society, hosted by
the University of Toronto, June 12  23, 1995](
Book
)
2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1997 in English and held by 2 WorldCat member libraries worldwide
Partial differential equations and their applications by
P. C Greiner(
Book
)
1 edition published in 1997 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 1997 in Undetermined and held by 1 WorldCat member library worldwide
Differentsial'nye uravneniia s chastnymi Proizvodnymi4 by
I︠U︡. V Egorov(
Book
)
1 edition published in 1988 in Russian and held by 1 WorldCat member library worldwide
1 edition published in 1988 in Russian and held by 1 WorldCat member library worldwide
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 SpringerLink (Service en ligne)
 Shubin, M. A. (Mikhail Aleksandrovich) 1944
 Egorov, ëIìU. V. (ëIìUriæi Vladimirovich) Author
 Seco, Luis A. Other
 Greiner, Peter G. Other
 Sulem, Catherine Other
 Egorov, IU. V. Author
 Sinha, P. C.
 Vsesoi︠u︡znyĭ institut nauchnoĭ i tekhnicheskoĭ informat︠s︡ii (Soviet Union)
 Greiner, Peter C. Author
Useful Links
Associated Subjects
Asymptotic expansions Boundary value problems Differential equations, Hyperbolic Differential equations, Partial Eigenvalues Elliptic operators Fiberings (Mathematics) Global analysis (Mathematics) Hamiltonian systems Initial value problems Mathematical analysis Mathematics Microlocal analysis Spectral theory (Mathematics)