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 Schrodinger 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. 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.
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Für höhere Schule und Studium
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ISBN-13
978-0-8218-1387-4 (9780821813874)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Klassifikation
On the scientific work of Mikhail Shlemovich Birman by V. Buslaev, M. Solomyak, and D. Yafaev List of publications of M. Sh. Birman Representation theorems for solutions of the Helmholtz equation on $\mathbb{R}^n$ by S. Agmon Kronig-Penney electron in a homogeneous electric field by V. S. Buslaev A Minkowski type trace inequality and strong subadditivity of quantum entropy by E. A. Carlen and E. H. Lieb Integrable operators by P. Deift On the determination of a potential from three spectra by F. Gesztesy and B. Simon Oscillatory eigenvalue branches for Schrodinger operators with strongly coupled magnetic fields by R. Hempel Schrodinger operators with strong magnetic fields: Quasi-periodicity of spectral orbits and topology by I. Herbst and S. Nakamura Heavy atoms in a superstrong magnetic field by V. Ivrii A parametrix for the nonstationary Schrodinger equation by L. Kapitanski and Yu. Safarov Comparison principles for nonlinear operator differential equations in Banach spaces by V. Kozlov and V. Maz'ya On disjointness of solutions to the MNS equations by O. A. Ladyzhenskaya and G. A. Seregin On the negative eigenvalues of a class of Schrodinger operators by A. Laptev and Yu. Netrusov Semiclassical asymptotics for the spectral shift function by D. Robert On the number of negative eigenvalues for the two-dimensional magnetic Schrodinger operator by G. Rozenblum and M. Solomyak Elliptic boundary value problems with relaxed conditions by M. A. Shubin On the spectrum of the periodic magnetic Hamiltonian by A. V. Sobolev Another look at Cwikel's inequality by T. Weidl The discrete spectrum in the singular Friedrichs model by D. Yafaev Spectrum of the relative motion of many-particle systems in a homogeneous magnetic field: What do we know about it? by G. Zhislin.
