Proceedings of Symposia in Pure Mathematics, Volume: 76
2007; 960 pp; hardcover
ISBN-10: 0-8218-3783-4
ISBN-13: 978-0-8218-3783-2
Expected publication date is March 31, 2007. Items contained in
this set are available for individual sale:
PSPUM/76.1 PSPUM/76.2
This Festschrift had its origins in a conference called SimonFest
held at Caltech, March 27-31, 2006, to honor Barry Simon's 60th
birthday. It is not a proceedings volume in the usual sense since
the emphasis of the majority of the contributions is on reviews
of the state of the art of certain fields, with particular focus
on recent developments and open problems. The bulk of the
articles in this Festschrift are of this survey form, and a few
review Simon's contributions to a particular area. Part 1
contains surveys in the areas of Quantum Field Theory,
Statistical Mechanics, Nonrelativistic Two-Body and N-Body
Quantum Systems, Resonances, Quantum Mechanics with Electric and
Magnetic Fields, and the Semiclassical Limit. Part 2 contains
surveys in the areas of Random and Ergodic Schrodinger Operators,
Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse
Spectral Theory. In several cases, this collection of surveys
portrays both the history of a subject and its current state of
the art. Exhaustive lists of references enhance the presentation
offered in these surveys.
A substantial part of the contributions to this Festschrift are
survey articles on the state of the art of certain areas with
special emphasis on open problems. This will benefit graduate
students as well as researchers who want to get a quick, yet
comprehensive introduction into an area covered in this volume.
Readership
Research mathematicians interested in mathematical physics and
spectral theory.
Table of Contents
Part I
Quantum field theory, statistical mechanics
M. Aizenman -- Perspectives in statistical mechanics
T. Chen and J. Frohlich -- Coherent infrared representations in
non-relativistic QED
B. Nachtergaele -- Quantum spin systems after DLS 1978
L. Rosen -- Barry Simon's contributions to quantum field theory
Nonrelativistic two-body and N-body quantum systems, resonances
M. S. Ashbaugh and R. D. Benguria -- Isoperimetric inequalities
for eigenvalues of the Laplacian
E. B. Davies -- Non-self-adjoint operators and pseudospectra
R. Froese -- Barry Simon's contribution to non-relativistic
quantum mechanics: Two-body and N-body Schrodinger operators and
resonances
C. Gerard -- N-body quantum scattering and quantum resonances: An
overview
G. A. Hagedorn and A. Joye -- Mathematical analysis of Born-Oppenheimer
approximations
E. M. Harrell II -- Perturbation theory and atomic resonances
since Schrodinger's time
A. Lenard -- On a theorem for quantum mechanical scattering
theory
V. Maz'ya -- Analytic criteria in the qualitative spectral
analysis of the Schrodinger operator
P. Perry -- The spectral geometry of geometrically finite
hyperbolic manifolds
Y. Pinchover -- Topics in the theory of positive solutions of
second-order elliptic and parabolic partial differential
equations
W. P. Reinhardt -- Complex scaling in atomic physics: A staging
ground for experimental mathematics and for extracting physics
from otherwise impossible computations
A. V. Sobolev -- Recent results on the Bethe-Sommerfeld
conjecture
Electric and magnetic fields, semiclassical limit
L. Erdos -- Recent developments in quantum mechanics with
magnetic fields
G. M. Graf -- Aspects of the integer quantum Hall effect
I. W. Herbst -- Barry Simon's work on electric and magnetic
fields and the semi-classical limit
D. Hundertmark -- Some bound state problems in quantum mechanics
Part II
Random and ergodic Schrodinger operators, singular continuous
spectrum
J. Bourgain -- A new approach to spectral gap problems
D. Damanik -- Strictly ergodic subshifts and associated operators
D. Damanik -- Lyapunov exponents and spectral analysis of ergodic
Schrodinger operators: A survey of Kotani theory and its
applications
S. A. Denisov and A. Kiselev -- Spectral properties of
Schrodinger operators with decaying potentials
M. Goldstein and W. Schlag -- On the formation of gaps in the
spectrum of Schrodinger operators with quasi-periodic potentials
S. Jitomirskaya -- Ergodic Schrodinger operators (on one foot)
W. Kirsch and B. Metzger -- The integrated density of states for
random Schrodinger operators
Y. Last -- Exotic spectra: A review of Barry Simon's central
contributions
Orthogonal polynomials, inverse spectral theory
P. Deift -- Riemann-Hilbert methods in the theory of orthogonal
polynomials
F. Gesztesy -- Inverse spectral theory as influenced by Barry
Simon
L. Golinskii and V. Totik -- Orthogonal polynomials: From Jacobi
to Simon
S. Khrushchev -- Orthogonal polynomials: The first minutes
R. Killip -- Spectral theory via sum rules
F. Gesztesy, P. Deift, C. Galvez, P. Perry, and W. Schlag --
Barry Simon's list of publications
Graduate Studies in Mathematics, Volume: 80
2007; 224 pp; hardcover
ISBN-10: 0-8218-4215-3
ISBN-13: 978-0-8218-4215-7
Expected publication date is April 26, 2007.
This is a textbook for a one-semester graduate course in measure-theoretic
probability theory, but with ample material to cover an ordinary
year-long course at a more leisurely pace. Khoshnevisan's
approach is to develop the ideas that are absolutely central to
modern probability theory, and to showcase them by presenting
their various applications. As a result, a few of the familiar
topics are replaced by interesting non-standard ones.
The topics range from undergraduate probability and classical
limit theorems to Brownian motion and elements of stochastic
calculus. Throughout, the reader will find many exciting
applications of probability theory and probabilistic reasoning.
There are numerous exercises, ranging from the routine to the
very difficult. Each chapter concludes with historical notes.
Readership
Graduate students interested in probability theory
Table of contents
2007; 336 pp; hardcover
ISBN-10: 0-8218-4224-2
ISBN-13: 978-0-8218-4224-9
Expected publication date is May 6, 2007.
In the spirit of The Book of the One Thousand and One Nights, the
authors offer 1001 problems in number theory in a way that
entices the reader to immediately attack the next problem.
Whether a novice or an experienced mathematician, anyone
fascinated by numbers will find a great variety of problems--some
simple, others more complex--that will provide them with a
wonderful mathematical experience.
Readership
Undergraduates and graduate students interested in number theory.
Table of Contents
Key elements from the theory
Statements of the problems
Solutions
Bibliography
Terminology index
Index of authors
History of Mathematics, Volume: 6
2007; approx. 300 pp; hardcover
ISBN-10: 0-8218-4261-7
ISBN-13: 978-0-8218-4261-4
Expected publication date is May 17, 2007.
This volume contains articles on the history of Soviet
mathematics, many of which are personal accounts by
mathematicians who witnessed and contributed to the turbulent and
glorious years of Moscow mathematics. The articles in the book
focus on mathematical developments in that era, the personal
lives of Russian mathematicians, and political events that shaped
the course of scientific work in the Soviet Union. Important
contributions include an article about Luzin and his school,
based in part on documents that were released only after
perestroika, and two articles on Kolmogorov. The volume concludes
with annotated bibliographies in English and Russian for further
reading.
The revised edition is appended by an article of Tikhomirov,
which provides an update and general overview of 20th-century
Moscow mathematics, and it also includes an Index of Names.
This book should appeal to mathematicians, historians, and anyone
else interested in Soviet mathematical history.
Co-published with the London Mathematical Society beginning with
Volume 4. Members of the LMS may order directly from the AMS at
the AMS member price. The LMS is registered with the Charity
Commissioners.
Readership
Undergraduates, graduate students and research mathematicians
interested in the history of mathematics, especially in Russia.
Table of Contents
A. P. Yushkevich -- Encounters with mathematicians
S. S. Demidov -- The Moscow school of the theory of functions in
the 1930s
E. M. Landis -- About mathematics at Moscow State University in
the late 1940s and early 1950s
B. A. Rosenfeld -- Reminiscences of Soviet mathematicians
V. M. Tikhomirov -- A. N. Kolmogorov
V. I. Arnol'd -- On A. N. Kolmogorov
M. M. Postnikov -- Pages of a mathematical autobiography (1942-1953)
B. A. Kushner -- Markov and Bishop: An essay in memory of A. A.
Markov (1903-1979) and E. Bishop (1928-1983)
I. Piatetski-Shapiro -- Etude on life and automorphic forms in
the Soviet Union
D. B. Fuchs -- On Soviet mathematics of the 1950s and 1960s
A. B. Sossinsky -- In the other direction
S. S. Demidov -- A brief survey of the literature on the
development of mathematics in the USSR
S. S. Demidov -- Russian bibliography
V. M. Tikhomirov -- Moscow mathematics--Then and now
Errata
Index of names
Mathematical Surveys and Monographs, Volume: 136.
2007; approx. 427 pp; hardcover
ISBN-10: 0-8218-3668-4
ISBN-13: 978-0-8218-3668-2
Expected publication date is May 11, 2007.
This book presents methods to study the controllability and the
stabilization of nonlinear control systems in finite and infinite
dimensions. The emphasis is put on specific phenomena due to
nonlinearities. In particular, many examples are given where
nonlinearities turn out to be essential to get controllability or
stabilization. Various methods are presented to study the
controllability or to construct stabilizing feedback laws. The
power of these methods is illustrated by numerous examples coming
from such areas as celestial mechanics, fluid mechanics, and
quantum mechanics.
The book is addressed to graduate students in mathematics or
control theory, and to mathematicians or engineers with an
interest in nonlinear control systems governed by ordinary or
partial differential equations.
Readership
Graduate students and research mathematicians interested in
control theory and nonlinear partial differential equations.
Table of Contents
Controllability of linear control systems
Finite-dimensional linear control systems
Linear partial differential equations
Controllability of nonlinear control systems
Controllability of nonlinear systems in finite dimension
Linearized control systems and fixed-point methods
Iterated Lie brackets
Return method
Quasi-static deformations
Power series expansion
Previous methods applied to a Schrodinger equation
Stabilization
Linear control systems in finite dimension and applications to
nonlinear control systems
Stabilization of nonlinear control systems in finite dimension
Feedback design tools
Applications to some partial differential equations
Elementary results on semigroups of linear operators
Degree theory
Bibliography
List of symbols
Index