William T. Ross, University of Richmond, VA, and Harold S. Shapiro, Royal Institute of Technology, Stockholm, Sweden

Generalized Analytic Continuation

Description
The theory of generalized analytic continuation studies continuations of meromorphic functions in situations where traditional theory says there is a natural boundary. This broader theory touches on a remarkable array of topics in classical analysis, as described in the book. The authors use the strong analogy with the summability of divergent series to motivate the subject. In this vein, for instance, theorems can be described as being "Abelian" or "Tauberian". The introductory overview carefully explains the history and context of the theory. The book addresses the following questions: (1) When can we say, in some reasonable way, that component functions of a meromorphic function on a disconnected domain, are "continuations" of each other? (2) What role do such "continuations" play in certain aspects of approximation theory and operator theory?

The authors begin with a review of the works of Poincare, Borel, Wolff, Walsh, and Goncar, on continuation properties of "Borel series" and other meromorphic functions that are limits of rapidly convergent sequences of rational functions. They then move on to the work of Tumarkin, who looked at the continuation properties of functions in the classical Hardy space of the disk in terms of the concept of "pseudocontinuation". Tumarkin's work was seen in a different light by Douglas, Shapiro, and Shields in their discovery of a characterization of the cyclic vectors for the backward shift operator on the Hardy space. The authors cover this important concept of "pseudocontinuation" quite thoroughly since it appears in many areas of analysis. They also add a new and previously unpublished method of "continuation" to the list, based on formal multiplication of trigonometric series, which can be used to examine the backward shift operator on many spaces of analytic functions. The book attempts to unify the various types of "continuations" and suggests some interesting open questions.

Contents

Overview
Notation and preliminaries
The Poincare example
Borel's ideas and their later development
Goncar continuation
Pseudocontinuation
A continuation involving almost periodic functions
Continuation by formal multiplication of series
Generalized analytic continuation
List of symbols
Bibliography
Index


Details:

Series: University Lecture Series, Volume: 25
Publication Year: 2002
ISBN: 0-8218-3175-5
Paging: 149 pp.
Binding: Softcover

Edited by: A. Galves, Universidade de Sao Paulo, Brazil,
J. K. Hale, Georgia Institute of Technology, Atlanta, GA,
and C. Rocha, Instituto Superior Tecnico, Lisbon, Portugal

Differential Equations and Dynamical Systems

Description
This volume contains contributed papers authored by participants of a Conference on Differential Equations and Dynamical Systems which was held at the Instituto Superior Tecnico (Lisbon, Portugal). The conference brought together a large number of specialists in the area of differential equations and dynamical systems and provided an opportunity to celebrate Professor Waldyr Oliva's 70th birthday, honoring his fundamental contributions to the field. The volume constitutes an overview of the current research over a wide range of topics, extending from qualitative theory for (ordinary, partial or functional) differential equations to hyperbolic dynamics and ergodic theory.

Contents

・J. F. Alves and J. Sousa Ramos -- Total variations and semiconjugacy
・J. M. Arrieta, N. Consul, and A. Rodriguez-Bernal -- Pattern formation from boundary reaction
・B. S. Bardin and S. D. Furta -- Asymptotics of periodic travelling waves of an infinite beam on a nonlinear elastic support
・L. Barreira and B. Saussol -- Variational principles for hyperbolic flows
・P. Collet -- Extensive quantities for infinite systems
・N. Consul and S. M. Oliva -- Synchronization in herbivorous population models with diffusion and delays
・P. D. Cordaro -- Approximate solutions in locally integrable structures
・E. de Faria -- Aspects of rigidity and universality in one-dimensional dynamics
・T. Faria and W. Huang -- Stability of periodic solutions arising from Hopf bifurcation for a reaction-diffusion equation 　　with time delay
・J. M. Ferreira -- On the stability and oscillatory behavior of a retarded functional equation
・B. Fiedler, C. Rocha, D. Salazar, and J. Sola-Morales -- Dynamics of piecewise-autonomous bistable parabolic equations
・G. Gallavotti -- Intermittency and time arrow in statistical mechanics and turbulence
・J. K. Hale and G. Raugel -- Galerkin methods and regularity
・A. Jacquemard and M.-A. Teixeira -- A note on rigid decompositions of reversible mappings
・L. A. C. Ladeira, S. H. J. Nicola, and P. Z. Taboas -- Periodic solutions of an impulsive differential system with delay: 　　An L^p approach
・B. Lani-Wayda -- Representing Poincare maps by return times
・J. Llibre, J. Sotomayor, and M. Zhitomirskii -- Impasse bifurcations of constrained systems
・L. de Loura -- Multipole series and differential equations
・N. Martins and J. Sousa Ramos -- Cuntz-Krieger algebras arising from linear mod one transformations
・F. Mercuri, P. Piccione, and D. V. Tausk -- Ordinary differential equations of Morse-Sturm type
・W. M. Oliva -- Morse-Smale semiflows, openness and A-stability
・P. Piccione and D. V. Tausk -- Constrained Lagrangians and degenerate Hamiltonians on manifolds: An index theorem
・R. Severino and J. Sousa Ramos -- Symbolic dynamics in nonlinear boundary value problems
・L. Silva and J. Sousa Ramos -- A genealogy for kneading sequences of two-piecewise monotonous maps of the interval

Details:

Series: Fields Institute Communications, Volume: 31
Publication Year: 2002
ISBN: 0-8218-2860-6
Paging: 353 pp.
Binding: Hardcover

Takeo Ohsawa, Nagoya University, Japan

Analysis of Several Complex Variables

Expected publication date is July 24, 2002

Description
One of the approaches to the study of functions of several complex variables is to use methods originating in real analysis. In this concise book, the author gives a lucid presentation of how these methods produce a variety of global existence theorems in the theory of functions (based on the characterization of holomorphic functions as weak solutions of the Cauchy-Riemann equations).

Emphasis is on recent results, including an L^2 extension theorem for holomorphic functions, that have brought a deeper understanding of pseudoconvexity and plurisubharmonic functions. Based on Oka's theorems and his schema for the grouping of problems, the book covers topics at the intersection of the theory of analytic functions of several variables and mathematical analysis.

It is assumed that the reader has a basic knowledge of complex analysis at the undergraduate level. The book would make a fine supplementary text for a graduate-level course on complex analysis.

Contents

Holomorphic functions
Rings of holomorphic functions and overline{partial} cohomology
Pseudoconvexity and plurisubharmonic functions
L^2 estimates and existence theorems
Solutions of the extension and division problems
Bergman kernels
Bibliography
Index

Details:

Series: Translations of Mathematical Monographs,Volume: 211
Subseries: Iwanami Series in Modern Mathematics
Publication Year: 2002
ISBN: 0-8218-2098-2
Paging: approximately 144 pp.
Binding: Softcover

Edited by: Atish Dabholkar, Sunil Mukhi, and Spenta R. Wadia, Tata Institute of Fundamental Research, Mumbai, India

Strings 2001

Expected publication date is July 19, 2002

Description
String theory, sometimes called the "Theory of Everything", has the potential to provide answers to key questions involving quantum gravity, black holes, supersymmetry, cosmology, singularities and the symmetries of nature.

This multi-authored book summarizes the latest results across all areas of string theory from the perspective of world-renowned experts, including Michael Green, David Gross, Stephen Hawking, John Schwarz, Edward Witten and others.

The book comes out of the "Strings 2001" conference, organized by the Tata Institute for Fundamental Research (Mumbai, India), the Abdus Salam ICTP (Trieste, Italy), and the Clay Mathematics Institute (Cambridge, MA, USA). Individual articles discuss the study of D-branes, black holes, string dualities, compactifications, Calabi-Yau manifolds, conformal field theory, noncommutative field theory, string field theory, and string phenomenology. Numerous references provide a path to previous findings and results.

Written for physicists and mathematicians interested in string theory, the volume is a useful resource for any graduate student or researcher working in string theory, quantum field theory, or related areas.

Titles in this series are published by the AMS for the Clay Mathematics Institute (Cambridge, MA).

Contents

R. Gopakumar, M. Headrick, and M. Spradlin -- Noncommutative solitons I
J. G. Russo -- Free energy and critical temperature in eleven dimensions
P. Horava -- On de Sitter entropy and string theory
C. M. Hull -- Strongly coupled gravity and conformal invariance
M. Aganagic, R. Gopakumar, S. Minwalla, and A. Strominger -- Noncommutative solitons II
N. R. Constable, R. C. Myers, and Tafjord -- Fuzzy funnels: Non-abelian brane intersections
S. P. Trivedi -- Magnetic branes and giant gravitons
P. Kraus -- String field theory and the Doverline{D} system
L. Rastelli, A. Sen, and B. Zwiebach -- Vacuum string field theory
D. Ghoshal -- Normalization of the boundary superstring field theory
K. Hori -- Mirror symmetry and some applications
S. Govindarajan and T. Jayaraman -- D-branes and vector bundles on Calabi-Yau manifolds: A view from the helix
M. R. Douglas -- D-branes and mathcal{N}=1 supersymmetry
I. Antoniadis -- String physics at low energies
S. Kachru -- Tunneling-mediated supersymmetry breaking
G. Aldazabal, S. Franco, L. E. Ibanez, R. Rabadan, and A. Uranga -- Physics at intersecting branes
E. Silverstein -- (A)dS backgrounds from asymmetric orientfolds
I. Ellwood and W. Taylor -- Gauge invariance and tachyon condensation in open string field theory
J. Majumder -- Non-BPS D-branes on a Calabi-Yau orbifold
S. Mukhi and N. V. Suryanarayana -- Ramond-Ramond couplings of noncommutative branes
S. S. Gubser and I. Mitra -- Instability of charged black holes in anti-de Sitter space
M. Cvetic, G. W. Gibbons, H. Lu, and C. N. Pope -- Resolved branes and M-theory on special holonomy spaces
H. Verlinde -- Some challenges for holography
D. Gross -- An exact prediction of mathcal{N}=4 SUSYM gauge theory and comparison with string theory
S. Das -- Bulk couplings to noncommutative branes
Y. Okawa and H. Ooguri -- Energy-momentum tensors in matrix theory and in noncommutative gauge theories
V. A. Kazakov -- Matrix model of two-dimensional black hole
A. Dhar and Y. Kitazawa -- Wilson lines in noncommutative gauge theories
S.-J. Rey -- Classical and planar limits in noncommutative field theories
S. L. Shatashvili -- On field theory of open strings, tachyon condensation and closed strings
G. Mandal and S. R. Wadia -- Brane-antibrane system and the tachyon potential from matrix model
S. W. Hawking -- ADS, CFT and cosmology
E. Witten -- Quantum gravity in de Sitter space
E. Gava, A. B. Hammou, J. F. Morales, and K. S. Narain -- D1/D5 systems in mathcal{N}=4 string theories
R. Argurio, A. Giveon, and A. Shomer -- String theory on {rm AdS}_3 and symmetric products
M. Bianchi, M. B. Green, and S. Kovacs -- Instantons and BPS Wilson loops
A. W. Peet -- More on singularity resolution
N. Dorey, T. Hollowood, and S. P. Kumar -- From {mathcal N}=4 to {mathcal N}=1: Exact results vs AdS/CFT
I. R. Klebanov -- Supergravity dual of a cascading confining gauge theory
S. Fredenhagen and V. Schomerus -- Brane dynamics in CFT backgrounds
C. Bachas -- D-branes in some near-horizon geometries
J. A. Harvey -- Topology of the gauge group in noncommutative gauge theory
D. Kutasov -- Comments on the thermodynamics of little string theory and two dimensional string theory
J. H. Schwarz -- Comments on Born-Infeld theory
A. Dabholkar, S. Mukhi, and S. R. Wadia -- Acknowledgments
A. Dabholkar, S. Mukhi, and S. R. Wadia -- List of participants

Details:

Series: Clay Mathematics Proceedings,Volume: 1
Publication Year: 2002
ISBN: 0-8218-2981-5
Paging: approximately 512 pp.
Binding: Softcover