**American Mathematical Society Translations - Series 2
Advances in the Mathematical Sciences**

1999; 285 pp; Hardcover

MSC: Primary 35;

Print ISBN: 978-0-8218-1387-4

Product Code: TRANS2/189

Print ISBN: 978-0-8218-1387-4

Product Code: TRANS2/189

List Price: $120.00

AMS Member Price: $96.00

MAA Member Price: $108.00

**Electronic ISBN: 978-1-4704-3400-7
Product Code: TRANS2/189.E**

List Price: $120.00

AMS Member Price: $96.00

MAA Member Price: $108.00

# Differential Operators and Spectral Theory: M. Sh. Birman’s 70th Anniversary Collection

Share this page *Edited by *
*V. Buslaev; M. Solomyak; D. Yafaev*

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.

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

## Differential Operators and Spectral Theory: M. Sh. Birman's 70th Anniversary Collection

- Cover Cover11
- Title page v6
- Copyright page vi7
- Contents vii8
- On the scientific work of Mikhail Shlëmovich Birman 110
- List of publications of M. Sh. Birman 1726
- Representation theorems for solutions of the Helmholtz equation on ℝⁿ 2736
- Kronig-Penney electron in a homogeneous electric field 4554
- A Minkowski type trace inequality and strong subadditivity of quantum entropy 5968
- Integrable operators 6978
- On the determination of a potential from three spectra 8594
- Oscillatory eigenvalue branches for Schrödinger operators with strongly coupled magnetic fields 93102
- Schrödinger operators with strong magnetic fields: Quasi-periodicity of spectral orbits and topology 105114
- Heavy atoms in the superstrong magnetic field 125134
- A parametrix for the nonstationary Schrödinger equation 139148
- Comparison principles for nonlinear operator differential equations in Banach spaces 149158
- On disjointness of solutions to the MNS equations 159168
- On the negative eigenvalues of a class of Schrödinger operators 173182
- Semiclassical asymptotics for the spectral shift function 187196
- On the number of negative eigenvalues for the two-dimensional magnetic Schrödinger operator 205214
- Elliptic boundary problems with relaxed conditions 219228
- On the spectrum of the periodic magnet Hamiltonian 233242
- Another look at Cwikel’s inequality 247256
- The discrete spectrum in the singular Friedrichs model 255264
- Spectrum of the relative motion of many-particle systems in a homogeneous magnetic field: What do we know about it? 275284
- Back Cover Back Cover1297