eBook ISBN:  9781470434007 
Product Code:  TRANS2/189.E 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470434007 
Product Code:  TRANS2/189.E 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 

Book DetailsAmerican Mathematical Society Translations  Series 2Advances in the Mathematical SciencesVolume: 189; 1999; 285 ppMSC: Primary 35
This volume contains a collection of original papers in mathematical physics, spectral theory, and differential equations. The papers are dedicated to the outstanding mathematician, Professor M. Sh. Birman, on the occasion of his 70th birthday. Contributing authors are leading specialists and close professional colleagues of Birman.
The main topics discussed are spectral and scattering theory of differential operators, trace formulas, and boundary value problems for PDEs. Several papers are devoted to the magnetic Schrödinger operator, which is within Birman's current scope of interests and recently has been studied extensively. Included is a detailed survey of his mathematical work and an updated list of his publications.
This book is aimed at graduate students and specialists in the abovementioned branches of mathematics and theoretical physicists. The biographical section will be of interest to readers concerned with the scientific activities of Birman and the history of those branches of analysis and spectral theory where his contributions were important and often decisive.
Features:
 The first detailed survey of Birman's mathematical work; includes an updated bibliography.
 New material on the history of some branches of analysis.
 Prominent authors: Lieb, Agmon, Deift, Simon, Ladyzhenskaya, and others.
 All original works, containing new results in fields of great current interest.
ReadershipGraduate students and research specialists working in mathematical physics, differential and integral equations, mathematical analysis and operator theory; mathematicians who are interested in the application of mathematical analysis to problems in mathematical and theoretical physics.

Table of Contents

Chapters

V. Buslaev, M. Solomyak and D. Yafaev — On the scientific work of Mikhail Shlëmovich Birman

List of publications of M. Sh. Birman

Shmuel Agmon — Representation theorems for solutions of the Helmholtz equation on $\mathbb {R}^n$

V. S. Buslaev — KronigPenney electron in a homogeneous electric field

Eric A. Carlen and Elliott H. Lieb — A Minkowski type trace inequality and strong subadditivity of quantum entropy

Percy Deift — Integrable operators

Fritz Gesztesy and Barry Simon — On the determination of a potential from three spectra

Rainer Hempel — Oscillatory eigenvalue branches for Schrödinger operators with strongly coupled magnetic fields

Ira Herbst and Shu Nakamura — Schrödinger operators with strong magnetic fields: Quasiperiodicity of spectral orbits and topology

Victor Ivrii — Heavy atoms in the superstrong magnetic field

L. Kapitanski and Yu. Safarov — A parametrix for the nonstationary Schrödinger equation

Vladimir Kozlov and Vladimir Maz’ya — Comparison principles for nonlinear operator differential equations in Banach spaces

O. A. Ladyzhenskaya and G. A. Seregin — On disjointness of solutions to the MNS equations

A. Laptev and Yu. Netrusov — On the negative eigenvalues of a class of Schrödinger operators

Didier Robert — Semiclassical asymptotics for the spectral shift function

G. Rozenblum and M. Solomyak — On the number of negative eigenvalues for the twodimensional magnetic Schrödinger operator

M. A. Shubin — Elliptic boundary problems with relaxed conditions

Alexander V. Sobolev — On the spectrum of the periodic magnetic Hamiltonian

Timo Weidl — Another look at Cwikel’s inequality

D. Yafaev — The discrete spectrum in the singular Friedrichs model

G. Zhislin — Spectrum of the relative motion of manyparticle systems in a homogeneous magnetic field: What do we know about it?


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This volume contains a collection of original papers in mathematical physics, spectral theory, and differential equations. The papers are dedicated to the outstanding mathematician, Professor M. Sh. Birman, on the occasion of his 70th birthday. Contributing authors are leading specialists and close professional colleagues of Birman.
The main topics discussed are spectral and scattering theory of differential operators, trace formulas, and boundary value problems for PDEs. Several papers are devoted to the magnetic Schrödinger operator, which is within Birman's current scope of interests and recently has been studied extensively. Included is a detailed survey of his mathematical work and an updated list of his publications.
This book is aimed at graduate students and specialists in the abovementioned branches of mathematics and theoretical physicists. The biographical section will be of interest to readers concerned with the scientific activities of Birman and the history of those branches of analysis and spectral theory where his contributions were important and often decisive.
Features:
 The first detailed survey of Birman's mathematical work; includes an updated bibliography.
 New material on the history of some branches of analysis.
 Prominent authors: Lieb, Agmon, Deift, Simon, Ladyzhenskaya, and others.
 All original works, containing new results in fields of great current interest.
Graduate students and research specialists working in mathematical physics, differential and integral equations, mathematical analysis and operator theory; mathematicians who are interested in the application of mathematical analysis to problems in mathematical and theoretical physics.

Chapters

V. Buslaev, M. Solomyak and D. Yafaev — On the scientific work of Mikhail Shlëmovich Birman

List of publications of M. Sh. Birman

Shmuel Agmon — Representation theorems for solutions of the Helmholtz equation on $\mathbb {R}^n$

V. S. Buslaev — KronigPenney electron in a homogeneous electric field

Eric A. Carlen and Elliott H. Lieb — A Minkowski type trace inequality and strong subadditivity of quantum entropy

Percy Deift — Integrable operators

Fritz Gesztesy and Barry Simon — On the determination of a potential from three spectra

Rainer Hempel — Oscillatory eigenvalue branches for Schrödinger operators with strongly coupled magnetic fields

Ira Herbst and Shu Nakamura — Schrödinger operators with strong magnetic fields: Quasiperiodicity of spectral orbits and topology

Victor Ivrii — Heavy atoms in the superstrong magnetic field

L. Kapitanski and Yu. Safarov — A parametrix for the nonstationary Schrödinger equation

Vladimir Kozlov and Vladimir Maz’ya — Comparison principles for nonlinear operator differential equations in Banach spaces

O. A. Ladyzhenskaya and G. A. Seregin — On disjointness of solutions to the MNS equations

A. Laptev and Yu. Netrusov — On the negative eigenvalues of a class of Schrödinger operators

Didier Robert — Semiclassical asymptotics for the spectral shift function

G. Rozenblum and M. Solomyak — On the number of negative eigenvalues for the twodimensional magnetic Schrödinger operator

M. A. Shubin — Elliptic boundary problems with relaxed conditions

Alexander V. Sobolev — On the spectrum of the periodic magnetic Hamiltonian

Timo Weidl — Another look at Cwikel’s inequality

D. Yafaev — The discrete spectrum in the singular Friedrichs model

G. Zhislin — Spectrum of the relative motion of manyparticle systems in a homogeneous magnetic field: What do we know about it?