V. M. Manuilov and E. V. Troitsky, Moscow State University, Russia
Hilbert C*-Modules
Description
Based on lectures delivered by the authors at Moscow State
University, this volume presents a detailed introduction to the
theory of Hilbert C^*-modules.
Hilbert C^*-modules provide a natural generalization of Hilbert
spaces arising when the field of scalars mathbf{C} is replaced by
an arbitrary C^*-algebra. The general theory of Hilbert C^*-modules
appeared more than 30 years ago in the pioneering papers of W.
Paschke and M. Rieffel and has proved to be a powerful tool in
operator algebras theory, index theory of elliptic operators, K-
and KK-theory, and in noncommutative geometry as a whole.
Alongside these applications, the theory of Hilbert C^*-modules
is interesting on its own.
In this book, the authors explain in detail the basic notions and
results of the theory, and provide a number of important examples.
Some results related to the authors' research interests are also
included. A large part of the book is devoted to structural
results (self-duality, reflexivity) and to nonadjointable
operators.
Most of the book can be read with only a basic knowledge of
functional analysis; however, some experience in the theory of
operator algebras makes reading easier.
Contents
Basic definitions
Operators on Hilbert modules
Hilbert modules over W^*-algebras
Reflexive Hilbert C^*-modules
Multipliers of A-compact operators. Structure results
Diagonalization of operators over C^*-algebras
Homotopy triviality of groups of invertible operators
Hilbert modules and KK-theory
Bibliography
Notation index
Index
Details:
Series: Translations of Mathematical Monographs, Volume: 226
Publication Year: 2005
ISBN: 0-8218-3810-5
Paging: 202 pp.
Binding: Hardcover
Edited by: Jose Burillo, Universitat Politecnica de Catalunya, Barcelona, Spain, Sean Cleary, The City College of New York (CUNY), NY, Murray Elder, University of St. Andrews, Fife, Scotland, Jennifer Taback, Bowdoin College, Brunswick, ME, and Enric Ventura, Universitat Politecnica de Catalunya, Barcelona, Spain
Geometric Methods in Group Theory
Expected publication date is May 1, 2005
Description
This volume presents articles by speakers and participants in two
AMS special sessions, Geometric Group Theory and Geometric
Methods in Group Theory, held respectively at Northeastern
University (Boston, MA) and at Universidad de Sevilla (Spain).
The expository and survey articles in the book cover a wide range
of topics, making it suitable for researchers and graduate
students interested in group theory.
Contents
M. Cardenas and F. F. Lasheras -- Properly 3-realizable groups: a
survey
A. Martino and S. O Rourke -- Free actions on mathbb{Z}^n-trees:
a survey
G. Levitt -- Characterizing rigid simplicial actions on trees
J. Gonzalez-Meneses -- Improving an algorithm to solve Multiple
Simultaneous Conjugacy Problems in braid groups
E. Godelle and L. Paris -- On singular Artin monoids
O. Bogopolski -- A surface groups analogue of a theorem of Magnus
V. Addepalli and E. C. Turner -- Shift automorphisms of finite
order
V. Shpilrain -- Counting primitive elements of a free group
R. Weidmann -- A rank formula for amalgamated products with
finite amalgam
D. Kahrobaei -- A simple proof of a theorem of Karrass and
Solitar
S. W. Margolis, J. Meakin, and Z. Sunik -- Distortion functions
and the membership problem for submonoids of groups and monoids
J. Belk and K.-U. Bux -- Thompson's group F is maximally
nonconvex
S. Cleary and J. Taback -- Seesaw words in Thompson's group F
X. Martin -- Piecewise-projective representation of Thompson's
group T
T. Dymarz -- Bijective quasi-isometries of amenable groups
I. Bumagin -- On definitions of relatively hyperbolic groups
G. Baumslag -- Embedding wreath-like products in finitely
presented groups. I
S. Cleary and J. Taback -- Metric properties of the lamplighter
group as an automata group
F. Dahmani -- An example of non-contracting weakly branch
automaton group
A. Akhmedov -- Travelling salesman problem in groups
Details:
Series: Contemporary Mathematics, Volume: 372
Publication Year: 2005
ISBN: 0-8218-3362-6
Paging: 230 pp.
Binding: Softcover
Edited by: O. Costin and M. D. Kruskal, Rutgers University, Piscataway, NJ, and A. Macintyre, University
of London, UK
Analyzable Functions and Applications
Expected publication date is May 1, 2005
Description
The theory of analyzable functions is a technique used to study a
wide class of asymptotic expansion methods and their applications
in analysis, difference and differential equations, partial
differential equations and other areas of mathematics.
Key ideas in the theory of analyzable functions were laid out by
Euler, Cauchy, Stokes, Hardy, E. Borel, and others. Then in the
early 1980s, this theory took a great leap forward with the work
of J. Ecalle. Similar techniques and concepts in analysis, logic,
applied mathematics and surreal number theory emerged at
essentially the same time and developed rapidly through the 1990s.
The links among various approaches soon became apparent and this
body of ideas is now recognized as a field of its own with
numerous applications.
This volume stemmed from the International Workshop on Analyzable
Functions and Applications held in Edinburgh (Scotland). The
contributed articles, written by many leading experts, are
suitable for graduate students and researchers interested in
asymptotic methods.
Contents
S. Ait-Mokhtar -- A singularly perturbed Riccati equation
T. Aoki, T. Kawai, T. Koike, and Y. Takei -- On global aspects of
exact WKB analysis of operators admitting infinitely many phases
M. Aschenbrenner and L. van den Dries -- Asymptotic differential
algebra
W. Balser and V. Kostov -- Formally well-posed Cauchy problems
for linear partial differential equations with constant
coefficients
F. Blais, R. Moussu, and J.-P. Rolin -- Non-oscillating integral
curves and o-minimal structures
B. Braaksma and R. Kuik -- Asymptotics and singularities for a
class of difference equations
O. Costin -- Topological construction of transseries and
introduction to generalized Borel summability
E. Delabaere -- Addendum to the hyperasymptotics for
multidimensional Laplace integrals
F. Diener and M. Diener -- Higher-order terms for the de Moivre-Laplace
theorem
J. Ecalle -- Twisted resurgence monomials and canonical-spherical
synthesis of local objects
A. Fruchard and E. Matzinger -- Matching and singularities of
canard values
B. Mudavanhu and R. E. O'Malley, Jr. -- On the renormalization
method of Chen, Goldenfeld, and Oono
S. P. Norton -- Generalized surreal numbers
C. Olive, D. Sauzin, and T. M. Seara -- Two examples of
resurgence
Details:
Series: Contemporary Mathematics, Volume: 373
Publication Year: 2005
ISBN: 0-8218-3419-3
Paging: approximately 376 pp.
Binding: Softcover
Emmanuel Lesigne, Universite Francois Rabelais, Tours, France
Heads or Tails: An Introduction to Limit Theorems in
Probability
Expected publication date is June 22, 2005
Description
Everyone knows some of the basics of probability, perhaps enough to play
cards. Beyond the introductory ideas, there are many wonderful results
that are unfamiliar to the layman, but which are well within our grasp
to understand and appreciate. Some of the most remarkable results in probability
are those that are related to limit theorems--statements about what happens
when the trial is repeated many times. The most famous of these is the
Law of Large Numbers, which mathematicians, engineers, economists, and
many others use every day.
In this book, Lesigne has made these limit theorems accessible by
stating everything in terms of a game of tossing of a coin: heads
or tails. In this way, the analysis becomes much clearer, helping
establish the reader's intuition about probability. Moreover,
very little generality is lost, as many situations can be
modelled from combinations of coin tosses.
This book is suitable for anyone who would like to learn more
about mathematical probability and has had a one-year
undergraduate course in analysis.
Contents
Prerequisites and overview
Modeling a probabilistic experiment
Random variables
Independence
The binomial distribution
The weak law of large numbers
The large deviations estimate
The central limit theorem
The moderate deviations estimate
The local limit theorem
The arcsine law
The strong law of large numbers
The law of the iterated logarithm
Recurrence of random walks
Epilogue
Biographies
Bibliography
Index
Details:
Series: Student Mathematical Library,Volume: 28
Publication Year: 2005
ISBN: 0-8218-3714-1
Paging: approximately 160 pp.
Binding: Softcover
Edited by: Alexander Barvinok, University of Michigan, Ann Arbor, MI, Matthias Beck, San Francisco State University, CA, Christian Haase, Duke University, Durham, NC, Bruce Reznick, University of Illinois at Urbana-Champaign, IL, and Volkmar Welker, Philipps-Universitat Marburg, Germany
Integer Points in Polyhedra
-- Geometry, Number Theory, Algebra, Optimization
Expected publication date is June 1, 2005
Description
The AMS-IMS-SIAM Summer Research Conference on Integer Points in
Polyhedra took place in Snowbird (UT). This proceedings volume
contains original research and survey articles stemming from that
event. Topics covered include commutative algebra, optimization,
discrete geometry, statistics, representation theory, and
symplectic geometry. The book is suitable for researchers and
graduate students interested in combinatorial aspects of the
above fields.
Contents
J. Agapito -- A weighted version of quantization commutes with
reduction for a toric manifold
M. Beck, J. A. De Loera, M. Develin, J. Pfeifle, and R. P.
Stanley -- Coefficients and roots of Ehrhart polynomials
B. Chen -- Ehrhart polynomials of lattice polyhedral functions
Y. Chen, I. Dinwoodie, A. Dobra, and M. Huber -- Lattice points,
contingency tables, and sampling
C. Cochet -- Kostka numbers and Littlewood-Richardson
coefficients
C. Haase -- Polar decomposition and Brion's theorem
P. Hersh and V. Welker -- Grobner basis degree bounds on Tor^{k[Lambda
]}_bullet(k,k)_bullet and discrete Morse theory for posets
J. B. Lasserre -- Integer programming duality and superadditive
functions
F. Santos -- The Cayley trick and triangulations of products of
simplices
M. Beck, B. Chen, L. Fukshansky, C. Haase, A. Knutson, B.
Reznick, S. Robins, and A. Schurmann -- Problems from the
Cottonwood Room
Details:
Series: Contemporary Mathematics, Volume: 374
Publication Year: 2005
ISBN: 0-8218-3459-2
Paging: 191 pp.
Binding: Softcover