Anatole Katok, Pennsylvania State University, University Park, PA

Combinatorial Constructions in Ergodic Theory and Dynamics

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

John Roe, Pennsylvania State University, University Park, PA

Lectures on Coarse Geometry

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

Edited by: Gerard J. Foschini, Lucent Technologies Bell Laboratories, Holmdel, NJ,
and Sergio Verdu, Princeton University, NJ

Multiantenna Channels: Capacity, Coding and Signal Processing

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


Edited by: Katsumi Nomizu, Brown University, Providence, RI

Selected Papers on Analysis and Differential Equations

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

Edited by: Geoffrey L. Price, Editor-in-Chief, and B. Mitchell Baker, U.S. Naval Academy, Annapolis, MD, and Palle E.T. Jorgensen and Paul S. Muhly, University of Iowa, Iowa City, IA

Advances in Quantum Dynamics

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