American Mathematical Society TranslationsSeries 2 Advances in the Mathematical Sciences 1999; 285 pp; hardcover Volume: 189 ISBN10: 0821813870 ISBN13: 9780821813874 List Price: US$120 Member Price: US$96 Order Code: TRANS2/189
 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.
Readership 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. Table of Contents  V. Buslaev, M. Solomyak, and D. Yafaev  On the scientific work of Mikhail Shlëmovich Birman
 List of publications of M. Sh. Birman
 S. Agmon  Representation theorems for solutions of the Helmholtz equation on \(\mathbb{R}^n\)
 V. S. Buslaev  KronigPenney electron in a homogeneous electric field
 E. A. Carlen and E. H. Lieb  A Minkowski type trace inequality and strong subadditivity of quantum entropy
 P. Deift  Integrable operators
 F. Gesztesy and B. Simon  On the determination of a potential from three spectra
 R. Hempel  Oscillatory eigenvalue branches for Schrödinger operators with strongly coupled magnetic fields
 I. Herbst and S. Nakamura  Schrödinger operators with strong magnetic fields: Quasiperiodicity of spectral orbits and topology
 V. Ivrii  Heavy atoms in a superstrong magnetic field
 L. Kapitanski and Yu. Safarov  A parametrix for the nonstationary Schrödinger equation
 V. Kozlov and V. 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
 D. 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 value problems with relaxed conditions
 A. V. Sobolev  On the spectrum of the periodic magnetic Hamiltonian
 T. 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?
