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Advances in the Mathematical Sciences
Differential Operators and Spectral Theory: M. Sh. Birman's 70th Anniversary Collection
Edited by: V. Buslaev, St. Petersburg State University, Russia, M. Solomyak, Weizmann Institute of Science, Rehovot, Israel, and D. Yafaev, Rennes University, France

American Mathematical Society Translations--Series 2
Advances in the Mathematical Sciences
1999; 285 pp; hardcover
Volume: 189
ISBN-10: 0-8218-1387-0
ISBN-13: 978-0-8218-1387-4
List Price: US$114
Member Price: US$91.20
Order Code: TRANS2/189
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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 above-mentioned 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.


  • 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.

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 -- Kronig-Penney 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: Quasi-periodicity 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 two-dimensional 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 many-particle systems in a homogeneous magnetic field: What do we know about it?
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