Expected publication date is November 12,
2003
Description
Ergodic theory studies measure-preserving
transformations of
measure spaces. These objects are intrinsically
infinite, and the
notion of an individual point or of an orbit
makes no sense.
Still there are a variety of situations when
a measure preserving
transformation (and its asymptotic behavior)
can be well
described as a limit of certain finite objects
(periodic
processes).
The first part of this book develops this
idea systematically.
Genericity of approximation in various categories
is explored,
and numerous applications are presented,
including spectral
multiplicity and properties of the maximal
spectral type. The
second part of the book contains a treatment
of various
constructions of cohomological nature with
an emphasis on
obtaining interesting asymptotic behavior
from approximate
pictures at different time scales.
The book presents a view of ergodic theory
not found in other
expository sources. It is suitable for graduate
students familiar
with measure theory and basic functional
analysis.
Contents
Approximation and genericity in ergodic theory
Cocycles, cohomology and combinatorial constructions
References
Details:
Series: University Lecture Series, Volume:
30
Publication Year: 2003
ISBN: 0-8218-3496-7
Paging: 121 pp.
Binding: Softcover
Expected publication date is November 16,
2003
Description
Coarse geometry is the study of spaces (particularly
metric
spaces) from a "large scale" point
of view, so that two
spaces that look the same from a great distance
are actually
equivalent. This point of view is effective
because it is often
true that the relevant geometric properties
of metric spaces are
determined by their coarse geometry. Two
examples of important
uses of coarse geometry are Gromov's beautiful
notion of a
hyperbolic group and Mostow's proof of his
famous rigidity
theorem.
The first few chapters of the book provide
a general perspective
on coarse structures. Even when only metric
coarse structures are
in view, the abstract framework brings the
same simplification as
does the passage from epsilons and deltas
to open sets when
speaking of continuity. The middle section
of the book reviews
notions of negative curvature and rigidity.
Modern interest in
large scale geometry derives in large part
from Mostow's rigidity
theorem and from Gromov's subsequent "large
scale"
rendition of the crucial properties of negatively
curved spaces.
The final chapters discuss recent results
on asymptotic dimension
and uniform embeddings into Hilbert space.
John Roe is known for his work on index theory,
coarse geometry,
and topology. His exposition is clear and
direct, bringing
insight to this modern field of mathematics.
Students and
researchers who wish to learn about contemporary
methods of
understanding the geometry and topology of
manifolds will be well
served by reading this book.
Also available from the AMS by John Roe is
Index Theory, Coarse
Geometry, and Topology of Manifolds.
Contents
Metric spaces
Coarse spaces
Growth and amenability
Translation algebras
Coarse algebraic topology
Coarse negative curvature
Limits of metric spaces
Rigidity
Asymptotic dimension
Groupoids and coarse geometry
Coarse embeddability
Bibliography
Details:
Series: University Lecture Series, Volume:
31
Publication Year: 2003
ISBN: 0-8218-3332-4
Paging: 175 pp.
Binding: Softcover
Expected publication date is November 22,
2003
Description
This volume is a collection of papers from
the DIMACS Workshop on
Signal Processing for Wireless Transmission.
The workshop brought
together theoreticians and practitioners
working on wireless
communications, information, and coding theory
from a variety of
perspectives. The main topics discussed in
the book are capacity
of multiantenna channels, vector broadcast
channels and "dirty-paper"
coding, signal processing, and ad hoc networking
in wideband
channels. These are all major themes in current
research in
physical-layer design for wireless communication.
The book is suitable for graduate students
and researchers
interested in mathematical problems of communication
theory.
Contents
Capacity of multiantenna channels
H. Xu, D. Chizhik, H. Huang, and R. Valenzuela
-- Broadband MIMO
channel model for realistic capacity and
system performance
evaluations
A. M. Tulino, A. Lozano, and S. Verdu --
Bandwidth-power tradeoff
of multi-antenna systems in the low-power
regime
A. L. Moustakas, S. H. Simon, and A. M. Sengupta
-- Distribution
of MIMO capacity in the presence of correlated
signals and
interferers: A (not so) large N analysis
S. H. Simon and A. L. Moustakas -- Optimality
of beamforming in
multiple transmitter multiple receiver communication
systems with
partial channel knowledge
Capacity of broadcast channels and dirty-paper
coding
N. Jindal, S. Vishwanath, S. Jafar, and A.
Goldsmith -- Duality,
dirty paper coding, and capacity for multiuser
wireless channels
D. Tse and P. Viswanath -- On the capacity
of the multiple
antenna broadcast channel
S. Vishwanath, G. Kramer, S. Shamai (Shitz),
S. Jafar, and A.
Goldsmith -- Capacity bounds for Gaussian
vector broadcast
channels
G. Caire and S. Shamai (Shitz) -- Writing
on dirty tape with LDPC
codes
G. J. Foschini and A. H. Diaz -- Dirty paper
coding: Perturbing
off the infinite dimensional lattice limit
Signal processing for multiantenna channels
B. Hassibi and H. Vikalo -- Maximum-likelihood
decoding and
integer least-squares: The expected complexity
D. Chizhik -- Slowing the time-fluctuating
MIMO channel
G. J. Foschini and M. Sellathurai -- A spacetime
architectural
superstructure enabling efficient multiple
antenna communication
E. Biglieri, A. Nordio, and G. Taricco --
Space-time coding with
iterative receiver interfaces
S. N. Diggavi, N. Al-Dhahir, and A. R. Calderbank
-- Diversity
order of space-time block codes in inter-symbol
interference
multiple-access channels
D. Samardzija and N. Mandayam -- Pilot assisted
estimation of
MIMO fading channel response and achievable
data rates
Networking capacity
Y. Souilmi and R. Knopp -- Challenges in
UWB signaling for adhoc
networking
I. Maric and R. Yates -- Efficient multihop
broadcast for
wideband systems
Details:
Series: DIMACS: Series in Discrete Mathematics
and Theoretical
Computer Science, Volume: 62
Publication Year: 2003
ISBN: 0-8218-3407-X
Paging: 299 pp.
Binding: Hardcover
Expected publication date is November 12,
2003
Description
This volume contains translations of papers
that originally
appeared in the Japanese journal, Sugaku.
Ordinarily the papers
would appear in the AMS translation of that
journal, but to
expedite publication, the Society has chosen
to publish them as a
volume of selected papers. The papers range
over a variety of
topics, including nonlinear partial differential
equations, C^*-algebras,
and Schrodinger operators.
The volume is suitable for graduate students
and research
mathematicians interested in analysis and
differential equations.
Contents
N. Ikeda -- Van Vleck formula for Wiener
integrals and Jacobi
fields
R. Kuwabara -- Spectral geometry for Schrodinger
operators in a
magnetic field
K. Matsumoto -- Symbolic dynamics and C^*-algebras
G. Nakamura -- Inverse problems for elasticity
Y. Shibata -- Time-global solutions of nonlinear
evolution
equations and their stability
K. Tachizawa -- Wavelets and eigenvalues
of Schrodinger operators
E. Yanagida and S. Yotsutani -- Recent topics
on nonlinear
partial differential equations: Structure
of radial solutions for
semilinear elliptic equations
Details:
Series: American Mathematical Society Translations--Series
2,
Volume: 211
Publication Year: 2003
ISBN: 0-8218-3508-4
Paging: 137 pp.
Binding: Hardcover
Expected publication date is December 27,
2003
Description
This volume contains the proceedings of the
conference on
Advances in Quantum Dynamics. The purpose
of the conference was
to assess the current state of knowledge
and to outline future
research directions of quantum dynamical
semigroups on von
Neumann algebras.
Since the appearance of the landmark papers
by F. Murray and J.
von Neumann, On the Rings of Operators, von
Neumann algebras have
been used as a mathematical model in the
study of time evolution
of quantum mechanical systems. Following
the work of M. H. Stone,
von Neumann, and others on the structure
of one-parameter groups
of unitary transformations, many researchers
have made
fundamental contributions to the understanding
of time-reversible
dynamical systems. This book deals with the
mathematics of time-irreversible
systems, also called dissipative systems.
The time parameter is
the half-line, and the transformations are
now endomorphisms as
opposed to automorphisms.
For over a decade, W. B. Arveson and R. T.
Powers have pioneered
the effort to understand the structure of
irreversible quantum
dynamical systems on von Neumann algebras.
Their papers in this
volume serve as an excellent introduction
to the theory. Also
included are contributions in other areas
which have had an
impact on the theory, such as Brownian motion,
dilation theory,
quantum probability, and free probability.
The volume is suitable for graduate students
and research
mathematicians interested in the dynamics
of quantum systems and
corresponding topics in the theory of operator
algebras.
Contents
W. Arveson -- Four lectures on noncommutative
dynamics
R. T. Powers -- Construction of E_0-semigroups
of mathfrak B(mathfrak
h) from CP-flows
B. V. R. Bhat -- Atomic dilations
F. Cipriani and J.-L. Sauvageot -- Strong
solutions to the
Dirichlet problem for differential forms:
A quantum dynamical
semigroup approach
D. E. Evans and P. R. Pinto -- Modular invariants
and their
fusion rules
R. Floricel -- A decomposition of E_0-semigroups
R. Gohm -- A duality between extension and
dilation
I. Hirshberg and J. Zacharias -- On the structure
of spectral
algebras and their generalizations
Y. Katayama and M. Takesaki -- Outer actions
of a countable
discrete amenable group on an AFD factor
T. Katsura -- A construction of C^*-algebras
from C^*-correspondences
Y. Kawahigashi -- Classification of operator
algebraic conformal
field theories
A. Kishimoto -- Rohlin property for flows
C. Kostler -- Survey on a quantum stochastic
extension of Stone's
theorem
D. Markiewicz -- Quantized convolution semigroups
P. S. Muhly and B. Solel -- A model for quantum
Markov semigroups
T. Oikhberg, H. P. Rosenthal, and E. Stormer
-- A predual
characterization of semi-finite von Neumann
algebras
S. Sakai -- Pure states on C^*-algebras
M. Skeide -- Commutants of von Neumann modules,
representations
of mathcal{B}^a(E) and other topics related
to product systems of
Hilbert modules
R. Speicher -- Non-commutative Brownian motions
B. Tsirelson -- Non-isomorphic product systems
Details:
Series: Contemporary Mathematics, IVolume:
335
Publication Year: 2003
ISBN: 0-8218-3215-8
Paging: approximately 336 pp.
Binding: Softcover