Edited by: Anastasios Mallios and Marina Haralampidou, University of Athens, Greece

Topological Algebras and Applications

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

Edited by: Estela A. Gavosto, University of Kansas, Lawrence, KS, Marianne K. Korten and Charles N. Moore, Kansas State University, Manhattan, KS, and Rodolfo H. Torres, University of Kansas, Lawrence, KS

Harmonic Analysis, Partial Differential Equations, and Related Topics

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



Edited by: Gui-Qiang Chen, Elton Hsu, and Mark Pinsky, Northwestern University, Evanston, IL

Stochastic Analysis and Partial Differential Equations

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


Edited by: John Milnor, Stony Brook University, NY

Collected Papers of John Milnor: Differential Topology

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

Kehe Zhu, State University of New York at Albany, NY

Operator Theory in Function Spaces: Second Edition

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