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
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
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
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