Contemporary Mathematics, Volume: 427
2007; 442 pp; softcover
ISBN-10: 0-8218-3868-7
ISBN-13: 978-0-8218-3868-6
The Fifth International Conference on Topological Algebras and
Applications was held in Athens, Greece, from June 27th to July 1st
of 2005. The main topic of the Conference was general theory of
topological algebras and its various applications, with emphasis
on the "non-normed" case. In addition to the study of
the internal structure of non-normed, and even non-locally convex
topological algebras, there are applications to other branches of
mathematics, such as differential geometry of smooth manifolds,
and mathematical physics, such as quantum relativity and quantum
cosmology. Operator theory of unbounded operators and related non-normed
topological algebras are intensively studied here. Other topics
presented in this volume are topological homological algebra,
topological algebraic geometry, sheaf theory and K-theory.
Readership
Graduate students and research mathematicians interested in
topological algebras.
Table of Contents
Z. Abdelali and M. Chidami -- Topologisation et multiplication
dans certaines algebres
M. Abel -- On Serre-Swan-Mallios theorem
M. Abel -- Topological algebras with idempotently pseudoconvex
von Neumann bornology
M. Amyari and M. S. Moslehian -- Hyers-Ulam-Rassias stability of
derivations on Hilbert C^*-Modules
J. Arhippainen -- On extensions of Stone-Weierstrass Theorem
H. Arizmendi, A. Carrillo, and L. Palacios -- On Q_t-algebras
F. Bagarello -- Some results on the algebraic approach to quantum
dynamics
S. J. Bhatt -- Topological algebras and differential structures
in C^*-algebras
S. J. Bhatt, A. Inoue, and H. Ogi -- On C^*-spectrality of
locally convex ^*-algebras in C^*-algebras
D. G. Birbas -- Ptak function, positive elements and the positive
cone of a unital LC *-algebra
J. Bonet -- Topologizable operators on locally convex spaces
A. J. C. Martin and M. Haralampidou -- On locally convex H^*-triple
systems
M. Chahboun -- Harmonic functional calculus in m-p-complete A- p-normed
algebras
R. Choukri -- A concept of finiteness in topological algebras
T. Chryssakis -- Square roots of strongly positive elements in
lmc algebras
A. Kinani -- Harmonic functions operating on contractions in m-convex
algebras
A. Kinani, M. A. Nejjari, and M. Oudadess -- Some
characterizations using cone notions in m-convex algebras
M. Fragoulopoulou, A. Inoue, and K.-D. Kursten -- On the
completion of a C^*-normed algebra under a locally convex algebra
topology
R. I. Hadjigeorgiou -- On Silov's idempotent theorem
M. Haralampidou -- On generalized Ambrose algebras
A. Y. Helemskii -- Tensor products in quantum functional analysis:
The non-matricial approach
A. Inoue, M. Takakura, and H. Ogi -- Unbounded conditional
expectations for O^*-algebras
M. Joita -- A Radon-Nikodym theorem for completely multi-positive
linear maps and its applications
A. Kokk -- Commutativity criteria for Gelfand-Mazur algebras
G. Lassner -- Topological algebras and quantum cosmology [the
Abstract]
A. L. Khlass and M. Oudadess -- Representation of extensions, of
\mathbb{C}, endowed with a discrete absolute value
M. Leinert -- Another proof of the Shirali-Ford theorem
A. Mallios -- On algebra spaces
A. Mallios and A. Oukhouya -- On combinatorially regular
topological algebras
A. Najmi -- Topological algebras with continuous characters
G. F. Nassopoulos -- Spectral decomposition and duality in
commutative locally C^*-algebras
L. Oubbi -- Locally A-convex algebras revisited
M. Oudadess -- On different versions of Vidav-Palmer theorem
A. Oukhouya -- On combinatorially regular Frechet algebra
O. Panova -- Description of closed maximal one-sided ideals in
several classes of real Gelfand-Mazur algebras
A. Y. Pirkovskii -- Strictly flat cyclic Frechet modules and
approximate identities
A. Y. Pirkovskii and Y. V. Selivanov -- Homologically trivial
Frechet algebras
C. P. Podara -- On strictly flat Frechet modules
N. V. Rao, T. V. Tonev, and E. T. Toneva -- Uniform algebra
isomorphisms and peripheral spectra
C. Trapani -- Bounded and strongly bounded elements in Banach
quasi *-algebras
Y. Tsertos -- On dual coordinate systems
W. Zelazko -- Operator algebras on locally convex spaces
Contemporary Mathematics, Volume: 428
2007; approx. 179 pp; softcover
ISBN-10: 0-8218-4093-2
ISBN-13: 978-0-8218-4093-1
This collection of contributed articles comprises the scientific
program of the fifth annual Prairie Analysis Seminar. All
articles represent important current advances in the areas of
partial differential equations, harmonic analysis, and Fourier
analysis. A range of interrelated topics is presented, with
articles concerning Painleve removability, pseudodifferential
operators, A_p weights, nonlinear Schrodinger equations, singular
integrals, the wave equation, the Benjamin-Ono equation, quasi-geostrophic
equations, quasiconformal mappings, integral inclusions, Bellman
function methods, weighted gradient estimates, Hankel operators,
and dynamic optimization problems.
Most importantly, the articles illustrate the fruitful
interaction between harmonic analysis, Fourier analysis, and
partial differential equations, and illustrate the successful
application of techniques and ideas from each of these areas to
the others.
Readership
Graduate student and research mathematicians interested in
partial differential equations.
Contents
Contemporary Mathematics, Volume: 429
2007; approx. 285 pp; softcover
ISBN-10: 0-8218-4059-2
ISBN-13: 978-0-8218-4059-7
This book is a collection of original research papers and
expository articles from the scientific program of the 2004-05
Emphasis Year on Stochastic Analysis and Partial Differential
Equations at Northwestern University. Many well-known
mathematicians attended the events and submitted their
contributions for this volume.
Topics from stochastic analysis discussed in this volume include
stochastic analysis of turbulence, Markov processes, microscopic
lattice dynamics, microscopic interacting particle systems, and
stochastic analysis on manifolds. Topics from partial
differential equations include kinetic equations, hyperbolic
conservation laws, Navier-Stokes equations, and Hamilton-Jacobi
equations. A variety of methods, such as numerical analysis,
homogenization, measure-theoretical analysis, entropy analysis,
weak convergence analysis, Fourier analysis, and Ito's calculus,
are further developed and applied. All these topics are naturally
interrelated and represent a cross-section of the most
significant recent advances and current trends and directions in
stochastic analysis and partial differential equations.
This volume is suitable for researchers and graduate students
interested in stochastic analysis, partial differential
equations, and related analysis and applications.
Readership
Graduate students and research mathematicians interested in
stochastic analysis and partical differential equations.
Table of Contents
A. Biryuk, W. Craig, and S. Ibrahim -- Construction of suitable
weak solutions of the Navier-Stokes equations
I. H. Biswas, E. R. Jakobsen, and K. H. Karlsen -- Error
estimates for finite difference-quadrature schemes for a class of
nonlocal Bellman equations with variable diffusion
W. Bo, B. Cheng, J. Du, B. Fix, E. George, J. Glimm, J. W. Grove,
X. Jia, H. Jin, H. Lee, Y. Li, X. Li, X. Liu, D. H. Sharp, L. Wu,
and Y. Yu -- Recent progress in the stochastic analysis of
turbulent mixing
V. Calvez, B. Perthame, and M. S. tabar -- Modified Keller-Segel
system and critical mass for the log interaction kernel
G.-Q. Chen, N. Even, and C. Klingenberg -- Entropy solutions to
conservation laws with discontinuous fluxes via microscopic
interacting particle systems
Z.-Q. Chen and R. Song -- Spectral properties of subordinate
processes in domains
P. Constantin -- Smoluchowski Navier-Stokes systems
S. Fang -- Recent developments in stochastic differential
equations
E. P. Hsu -- Heat equations on manifolds and Bismut's formula
N. Ikeda and Y. Ogura -- On a class of one-dimensional Markov
processes with continuous paths
M. A. Katsoulakis, A. J. Majda, and A. Sopasakis -- Prototype
hybrid couplings of macroscopic deterministic models and
microscopic stochastic lattice dynamics
E. Kosygina -- Homogenization of stochastic Hamilton-Jacobi
equations: Brief review of methods and applications
P. Michel -- General relative entropy in a nonlinear McKendrick
model
M. A. Pinsky -- Pointwise Fourier inversion in analysis and
geometry
S. Taniguchi -- Stochastic analysis and the KdV equation
K. Trivisa -- On binary fluid mixtures
Collected Works, Volume: 19
2007; 329 pp; hardcover
ISBN-10: 0-8218-4230-7
ISBN-13: 978-0-8218-4230-0
The field of differential topology underwent a dramatic
development period between 1955 and 1965. This collection of
articles written by one of the creators of this field contains
not only original papers, but also previously unpublished
expository lectures. It includes commentary by the author,
filling in some of the historical context, and outlining
subsequent developments. It includes a rich bibliography of newer
and older papers, providing a wider and deeper understanding of
the subject. It also outlines the actual state of the art, and
provides an index that will allow the reader to browse easily
through the book.
Of particular interest are the articles related to the existence
of exotic differentiable structures on spheres, the achievement
for which J. Milnor was awarded the Fields Medal in 1962.
Readership
Graduate students and research mathematicians interested in
differential and algebriac topology.
Table of Contents
Exotic spheres
Introduction: How these papers came to be written
On manifolds homeomorphic to the 7-sphere
On the relationship between differentiable manifolds and
combinatorial manifolds
Sommes de varietes differentiables et structures differentiables
des spheres
Differentiable structures on spheres
A procedure for killing homotopy groups of differentiable
manifolds
Differentiable manifolds which are homotopy spheres
with M. A. Kervaire, Groups of homotopy spheres: I
Differential topology
Expository lectures
Introduction
with J. R. Munkres, Lectures on differential topology (Notes by J.
R. Munkres)
Lectures on differentiable structures
Smooth manifolds with boundary
Relations with algebraic topology
Introduction
with R. Bott, On the parallelizability of the spheres
Some consequences of a theorem of Bott
On the Whitehead homomorphism J
with M. A. Kervaire, Bernoulli numbers, homotopy groups and a
theorem of Rohlin
Cobordism
Introduction
On the cobordism ring \Omega*
On the cobordism ring \Omega* and a complex analogue, part I
Travaux de Milnor sur le cobordisme
A survey of cobordism theory
A survey of cobordism (Erratum)
Spin structures on manifolds
Remarks concerning spin manifolds
On the Stiefel-Whitney numbers of complex manifolds and of spin
manifolds
A concluding amusement: Symmetry breaking
Bibliography
Index
Mathematical Surveys and Monographs, Volume: 138
2007; 348 pp; hardcover
ISBN-10: 0-8218-3965-9
ISBN-13: 978-0-8218-3965-2
This book covers Toeplitz operators, Hankel operators, and
composition operators on both the Bergman space and the Hardy
space. The setting is the unit disk and the main emphasis is on
size estimates of these operators: boundedness, compactness, and
membership in the Schatten classes.
Most results concern the relationship between operator-theoretic
properties of these operators and function-theoretic properties
of the inducing symbols. Thus a good portion of the book is
devoted to the study of analytic function spaces such as the
Bloch space, Besov spaces, and BMOA, whose elements are to be
used as symbols to induce the operators we study.
The book is intended for both research mathematicians and
graduate students in complex analysis and operator theory. The
prerequisites are minimal; a graduate course in each of real
analysis, complex analysis, and functional analysis should
sufficiently prepare the reader for the book. Exercises and
bibliographical notes are provided at the end of each chapter.
These notes will point the reader to additional results and
problems.
Kehe Zhu is a professor of mathematics at the State University of
New York at Albany. His previous books include Theory of Bergman
Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and
Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005).
His current research interests are holomorphic function spaces
and operators acting on them.
Readership
Graduate students and research mathematicians interested in
complex analysis and operator theory.
Table of Contents
Bounded linear operators
Interpolation of Banach spaces
Integral operators on L^p spaces
Bergman spaces
Bloch and Besov spaces
The Berezin transform
Toeplitz operators on the Bergman space
Hankel operators on the Bergman space
Hardy spaces and BMO
Hankel operators on the Hardy space
Composition operators
Bibliography
Index