N. V. Krylov, University of Minnesota, Minneapolis, MN
Introduction to the Theory of Random Processes
Expected publication date is April 11, 2002
Description
This book concentrates on some general facts
and ideas of the
theory of stochastic processes. The topics
include the Wiener
process, stationary processes, infinitely
divisible processes,
and Ito stochastic equations.
Basics of discrete time martingales are also
presented and then
used in one way or another throughout the
book. Another common
feature of the main body of the book is using
stochastic
integration with respect to random orthogonal
measures. In
particular, it is used for spectral representation
of
trajectories of stationary processes and
for proving that
Gaussian stationary processes with rational
spectral densities
are components of solutions to stochastic
equations. In the case
of infinitely divisible processes, stochastic
integration allows
for obtaining a representation of trajectories
through jump
measures. The Ito stochastic integral is
also introduced as a
particular case of stochastic integrals with
respect to random
orthogonal measures.
Although it is not possible to cover even
a noticeable portion of
the topics listed above in a short book,
it is hoped that after
having followed the material presented here,
the reader will have
acquired a good understanding of what kind
of results are
available and what kind of techniques are
used to obtain them.
With more than 100 problems included, the
book can serve as a
text for an introductory course on stochastic
processes or for
independent study.
Other works by this author published by the
AMS include, Lectures
on Elliptic and Parabolic Equations in Holder
Spaces and
Introduction to the Theory of Diffusion Processes.
Contents
Generalities
The Wiener process
Martingales
Stationary processes
Infinitely divisible processes
Ito stochastic integral
Bibliography
Index
Details:
Series: Graduate Studies in Mathematics,Volume:
43
Publication Year: 2002
ISBN: 0-8218-2985-8
Paging: approximately 240 pp.
Binding: Hardcover
Jim Agler, University of California at San Diego, CA,
and John E. McCarthy, Washington University,
St. Louis, MO
Pick Interpolation and Hilbert Function Spaces
Expected publication date is April 4, 2002
Description
The book first rigorously develops the theory
of reproducing
kernel Hilbert spaces. The authors then discuss
the Pick problem
of finding the function of smallest $H^\infty$
norm that has
specified values at a finite number of points
in the disk. Their
viewpoint is to consider $H^\infty$ as the
multiplier algebra of
the Hardy space and to use Hilbert space
techniques to solve the
problem. This approach generalizes to a wide
collection of spaces.
The authors then consider the interpolation
problem in the space
of bounded analytic functions on the bidisk
and give a complete
description of the solution. They then consider
very general
interpolation problems. The book includes
developments of all the
theory that is needed, including operator
model theory, the
Arveson extension theorem, and the hereditary
functional calculus.
Contents
Prerequisites and notation
Introduction
Kernels and function spaces
Hardy spaces
$P^2(\mu)$
Pick redux
Qualitative properties of the solution of
the Pick problem in
$H^\infty(\mathbb{D})$
Characterizing kernels with the complete
Pick property
The universal Pick kernel
Interpolating sequences
Model theory I: Isometries
The bidisk
The extremal three point problem on $\mathbb{D}^2$
Collections of kernels
Model theory II: Function spaces
Localization
Schur products
Parrott's lemma
Riesz interpolation
The spectral theorem for normal $m$-tuples
Bibliography
Index
Details:
Series: Graduate Studies in Mathematics,Volume:
44
Publication Year: 2002
ISBN: 0-8218-2898-3
Paging: approximately 328 pp.
Binding: Hardcover
Toshitaki Kohno, University of Tokyo, Japan
Conformal Field Theory and Topology
Expected publication date is May 11, 2002
Description
Geometry and physics have been developed
with a strong influence
on each other. One of the most remarkable
interactions between
geometry and physics since 1980 has been
an application of
quantum field theory to topology and differential
geometry. This
book focuses on a relationship between two-dimensional
quantum
field theory and three-dimensional topology
which has been
studied intensively since the discovery of
the Jones polynomial
in the middle of the 1980s and Witten's invariant
for 3-manifolds
derived from Chern-Simons gauge theory. An
essential difficulty
in quantum field theory comes from infinite-dimensional
freedom
of a system. Techniques dealing with such
infinite-dimensional
objects developed in the framework of quantum
field theory have
been influential in geometry as well. This
book gives an
accessible treatment for a rigorous construction
of topological
invariants originally defined as partition
functions of fields on
manifolds.
The book is organized as follows: The Introduction
starts from
classical mechanics and explains basic background
materials in
quantum field theory and geometry. Chapter
1 presents conformal
field theory based on the geometry of loop
groups. Chapter 2
deals with the holonomy of conformal field
theory. Chapter 3
treats Chern-Simons perturbation theory.
The final chapter
discusses topological invariants for 3-manifolds
derived from
Chern-Simons perturbation theory.
Contents
Geometric aspects of conformal field theory
Jones-Witten theory
Chern-Simons perturbation theory
Further developments and prospects
Bibliography
Index
Details:
Series: Translations of Mathematical Monographs,Volume:
210
Publication Year: 2002
ISBN: 0-8218-2130-X
Paging: approximately 184 pp.
Binding: Softcover
Edited by: Donald M. Davis, Lehigh University, Bethlehem, PA,
Jack Morava, Johns Hopkins University, Baltimore,
MD,
Goro Nishida, Kyoto University, Japan,
W. Stephen Wilson, Johns Hopkins University,
Baltimore, MD,
and Nobuaki Yagita, Ibaraki University, Japan
Recent Progress in Homotopy Theory
Expected publication date is March 14, 2002
Description
This volume presents the proceedings from
the month-long program
held at Johns Hopkins University (Baltimore,
MD) on homotopy
theory, sponsored by the Japan-U.S. Mathematics
Institute (JAMI).
The book centers on the following:
1. classical and nonclassical theory of $H$-spaces,
compact
groups, and finite groups,
2. classical and chromatic homotopy theory
and localization,
3. classical and topological Hochschild cohomology,
4. elliptic cohomology and its relation to
Moonshine and
topological modular forms, and
5. motivic cohomology and Chow rings.
It surveys the current state of research
in homotopy theory and
suggests a framework for future developments.
The book begins
with two historical accounts, of the work
of Professors Peter
Landweber and Stewart Priddy, in honor of
their sixtieth
birthdays.
Contents
Two papers on the history of topology
H. Miller -- A marriage of manifolds and
algebra: The
mathematical work of Peter Landweber
N. Minami -- Some mathematical influences
of Stewart Priddy
Research papers
M. Bendersky and R. D. Thompson -- Some properties
of the $K$-theory
completion
R. R. Bruner, D. M. Davis, and M. Mahowald
-- Nonimmersions of
real projective spaces implied by $tmf$
M. Brunetti -- High Euler characteristics
for almost extraspecial
$p$-groups
Y. Hemmi -- Unstable $p$-th order operation
and $H$-spaces
M. Mahowald and M. Hopkins -- The structure
of 24 dimensional
manifolds having normal bundles which lift
to $BO[8]$
P. Hu and I. Kriz -- The homology of $BPO$
M. Inoue -- $\mathcal{A}$-generators of the
cohomology of the
Steinberg summand $M(n)$
J. P. Lin -- Commutators in the homology
of $H$-spaces
J. E. McClure and J. H. Smith -- A solution
of Deligne's
Hochschild cohomology conjecture
M. Mimura and T. Nishimoto -- Hopf algebra
structure of Morava
$K$-theory of the exceptional Lie groups
J. Martino and S. Priddy -- Minami-Webb type
decompositions for
compact Lie groups
D. C. Ravenel -- The method of infinite descent
in stable
homotopy theory I
K. Shimomura -- The homotopy groups $\pi_*(L_nT(m)\wedge
V(n-2))$
D. Tamaki -- The fiber of iterated Freudenthal
suspension and
Morava K-theory of $\Omega^kS^{2\ell+1}$
M. Tanabe -- On $K$-flat and $K$-moonshine-like
elements in
elliptic cohomology
T. Torii -- The geometric fixed point spectrum
of $({\mathbf Z}/p)^k$
Borel cohomology for $E_n$ and its completion
V. Voevodsky -- A possible new approach to
the motivic spectral
sequence for algebraic K-theory
C. W. Wilkerson, Jr. -- Rings of invariants
and inseparable forms
of algebras over the Steenrod algebra
N. Yagita -- Chow rings of classifying spaces
of extraspecial $p$
groups
Details:
Series: Contemporary Mathematics,Volume:
293
Publication Year: 2002
ISBN: 0-8218-2801-0
Paging: 409 pp.
Binding: Softcover