Yuli Eidelman and Vitali Milman, Tel Aviv University, Israel,
and Antonis Tsolomitis, University of the Aegean, Samos, Greece

Functional Analysis: An Introduction

Expected publication date is December 16, 2004

Description

This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators.

The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially self-contained. Prerequisites for the first part are minimal amounts of linear algebra and calculus. For the second part, some knowledge of topology and measure theory is recommended. Each of the 11 chapters is followed by numerous exercises, with solutions given at the end of the book.

The amount of mathematics presented in the book can well be absorbed in a year's study and will provide a sound basis for future reading. It is suitable for graduate students and researchers interested in operator theory and functional analysis.

Contents
Hilbert spaces and basic operator theory
Linear spaces; normed spaces; first examples
Hilbert spaces
The dual space
Bounded linear operators
Spectrum. Fredholm theory of compact operators
Self-adjoint operators
Functions of operators; spectral decomposition
Basics of functional analysis
Spectral theory of unitary operators
The fundamental theorems and the basic methods
Banach algebras
Unbounded self-adjoint and symmetric operators in H
Solutions to exercises
Bibliography
Symbols index
Subject index

Details:

Series: Graduate Studies in Mathematics, Volume: 66
Publication Year: 2004
ISBN: 0-8218-3646-3
Paging: approximately 344 pp.
Binding: Hardcover

Edited by: Anthony To-Ming Lau and Volker Runde, University of Alberta, Edmonton, AB, Canada

Banach Algebras and Their Applications

Expected publication date is December 30, 2004

Description

This proceedings volume is from the international conference on Banach Algebras and Their Applications held at the University of Alberta (Edmonton). It contains a collection of refereed research papers and high-level expository articles that offer a panorama of Banach algebra theory and its manifold applications.

Topics in the book range from K-theory to abstract harmonic analysis to operator theory. It is suitable for graduate students and researchers interested in Banach algebras.

Contents

M. Amini and A. Medghalchi -- Fourier algebras on tensor hypergroups
O. Yu. Aristov -- Amenability and compact type for Hopf-von Neumann algebras from the homological point of view
A. Baklouti, N. B. Salah, and K. Smaoui -- Some uncertainty principles on nilpotent Lie groups
D. P. Blecher -- Are operator algebras Banach algebras?
C.-H. Chu -- Jordan Banach algebras in harmonic analysis
J. Esterle -- Zero-one and zero-two laws for the behavior of semigroups near the origin
J. F. Feinstein and H. Kamowitz -- Compact homomorphisms between Dales-Davie algebras
B. Forrest -- Completely bounded multipliers and ideals in A(G) vanishing on closed subgroups
F. Gourdeau, Z. A. Lykova, and M. C. White -- The simplicial cohomology of L^1(mathbf{R}^k_+)
S. A. Grigoryan and T. V. Tonev -- Shift-invariant algebras on groups
N. Gronbak -- Self-induced Banach algebras
A. Ya. Helemskii -- Some aspects of topological homology since 1995: a survey
E. Kaniuth and T.-M. Lau -- Fourier algebras and amenability
W. C. Lang -- Refinement equations and generalized multiresolution analyses for hypergroups
R. Lasser -- Almost periodic sequences with respect to orthogonal polynomials
N. J. Laustsen -- K-theory for Banach *-algebras
V. Losert -- Separation property, Mautner phenomenon, and neutral subgroups
J. Mashreghi and T. Ransford -- Using entire functions to analyse power growth
M. Mathieu -- Another automatic boundedness technique
R. Meyer -- Bornological versus topological analysis in metrizable spaces
T. L. Miller, V. G. Miller, and M. M. Neumann -- Banach algebras, local spectral theory, and extensions of operators
W. J. Ricker -- Banach algebras of p-multiplier operators for the circle group
E. R. Schulz and K. F. Taylor -- Projections in L^1-algebras and tight frames
Yu. V. Selivanov -- Classes of Banach algebras of global dimension infinity
N. Spronk -- Representations of multiplier algebras in spaces of completely bounded maps

Details:

Series: Contemporary Mathematics, Volume: 363
Publication Year: 2004
ISBN: 0-8218-3471-1
Paging: 343 pp.
Binding: Softcover

Edited by: Mark Agranovsky, Bar-Ilan University, Ramat-Gan, Israel, Lavi Karp and David Shoikhet, ORT Braude College, Karmiel, Israel, and Lawrence Zalcman, Bar-Ilan University, Ramat-Gan, Israel

Complex Analysis and Dynamical Systems

Expected publication date is December 10, 2004

Description

This book contains contributions from the participants of an International Conference on Complex Analysis and Dynamical Systems.

The papers collected here are devoted to various topics in complex analysis and dynamical systems, ranging from properties of holomorphic mappings to attractors in hyperbolic spaces. Overall, these selections provide an overview of activity in analysis at the outset of the twenty-first century. The book is suitable for graduate students and researchers in complex analysis and related problems of dynamics.

With this volume, the Israel Mathematical Conference Proceedings are now published as a subseries of the AMS Contemporary Mathematics series.

Contents

L. Aizenberg -- Remarks on the "asymptotic maximum principle"
C. Beneteau and B. Korenblum -- Some coefficient estimates for H^p functions
R. Brooks -- A statistical model of Riemann surfaces
M. Budzynska -- Holomorphic retracts in domains with the locally uniformly linearly convex Kobayashi distance
M. Budzynska and T. Kuczumow -- Common fixed points of holomorphic mappings and retracts of B^infty_H
M. Elin, A. Goldvard, S. Reich, and D. Shoikhet -- Dynamics of spirallike functions
L. A. Harris -- Invertibility preserving linear maps of Banach algebras
J. Hilgert and D. Mayer -- The dynamical zeta function and transfer operators for the Kac-Baker model
V. A. Khatskevich, V. A. Senderov, and V. S. Shulman -- On operator matrices generating linear fractional maps of operator balls
T. Krainer and B.-W. Schulze -- Long-time asymptotics with geometric singularities in the spatial variables
S. L. Krushkal -- Grunsky inequalities of higher rank with applications to complex geometry and function theory
M. Lanza de Cristoforis -- Asymptotic behaviour of the conformal representation of a Jordan domain with a small hole and relative capacity
D. Lenz -- Singular continuous spectrum for certain quasicrystal Schrodinger operators
E. Malinnikova -- Measures orthogonal to the gradients of harmonic functions
O. Martio, V. Ryazanov, U. Srebro, and E. Yakubov -- Q-homeomorphisms
B. Paneah -- Dynamic methods in the general theory of Cauchy type functional equations
V. S. Rabinovich -- Exponential estimates for eigenfunctions of Schrodinger operators with rapidly increasing and discontinuous potentials
S. Reich and A. J. Zaslavski -- A porosity result for attracting mappings in hyperbolic spaces
B. Schneider and M. Shapiro -- Some properties of the quaternionic Cauchy-type integral for a piece-wise Liapunov surface of integration

Details:

Series: Contemporary Mathematics,Volume: 364
Publication Year: 2004
ISBN: 0-8218-3686-2
Paging: 260 pp.
Binding: Softcover

John Hempel, Rice University, Houston, TX

3-Manifolds

Expected publication date is November 27, 2004

From a review of the original edition:

"A careful and systematic development of the theory of the topology of 3-manifolds, focusing on the critical role of the fundamental group in determining the topological structure of a 3-manifold ... self-contained ... one can learn the subject from it ... would be very appropriate as a text for an advanced graduate course or as a basis for a working seminar."

-- MathSciNet

Description
For many years, John Hempel's book has been a standard text on the topology of 3-manifolds. Even though the field has grown tremendously during that time, the book remains one of the best and most popular introductions to the subject.

The theme of this book is the role of the fundamental group in determining the topology of a given 3-manifold. The essential ideas and techniques are covered in the first part of the book: Heegaard splittings, connected sums, the loop and sphere theorems, incompressible surfaces, free groups, and so on. Along the way, many useful and insightful results are proved, usually in full detail. Later chapters address more advanced topics, including Waldhausen's theorem on a class of 3-manifolds that is completely determined by its fundamental group. The book concludes with a list of problems that were unsolved at the time of publication.

Hempel's book remains an ideal text to learn about the world of 3-manifolds. The prerequisites are few and are typical of a beginning graduate student. Exercises occur throughout the text.

Other key books on low-dimensional topology available from the AMS are Knots and Links, Lectures on Three-Manifold Topology, and The Knot Book.

Contents

Preliminaries
Heegaard splittings
Connected sums
The loop and sphere theorems
Free groups
Incompressible surfaces
Kneser's conjecture on free products
Finitely generated subgroups
More on connected sums; Finite and abelian subgroups
I-bundles
Group extensions and fibrations
Seifert fibered spaces
Classification of P^2-irreducible, sufficiently large 3-manifolds
Some approaches to the Poincare conjecture
Open problems
References
Index
Symbols and notation

Details:

Series: AMS Chelsea Publishing
Publication Year: 2004
ISBN: 0-8218-3695-1
Paging: 195 pp.
Binding: Hardcover