Forster, Karl-Heinz; Jonas, Peter; Langer, Heinz (Eds.)

Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems

Series: Operator Theory: Advances and Applications, Vol. 162
2006, Approx. 315 p., Hardcover
ISBN: 3-7643-7452-7

About this book

This volume contains a collection of recent original research papers in operator theory in Krein spaces, on generalized Nevanlinna functions, which are closely connected with this theory, and on nonlinear eigenvalue problems.

Key topics:
- spectral theory for normal operators in Krein spaces
- perturbation theory for selfadjoint operators in Krein spaces
- models for generalized Nevanlinna functions

Written for:
Postgraduates and researchers interested in functional analysis, differential operators and function theory

Table of contents

Preface.- Contributions by V. Adamyan, D. Alpay, Y. Arlinskii, P. Binding, J.F. Brasche, R. Denk, V. Derkach, A. Dijksma, K.-H. Forster, S. Hassi, R. Hryniv, P. Jonas, M. Kaltenback, L. Klotz, H. Langer, M. Langer, H. Lasarow, A. Luger, M.M. Malamud, C. Mehl, M. Moller, B. Nagy, H. Neidhardt, A.C.M. Ran, L. Rodman, M. Shapiro, H. de Snoo, F.H. Szafraniec, C. Tretter, K. Veselic, D. Volok, G. Wanjala, H. Winkler, and H. Woracek




Ginzburg, Victor (Ed.)

Algebraic Geometry and Number Theory
In Honor of Vladimir Drinfeld's 50th Birthday

Series: Progress in Mathematics, Preliminary entry 850
2006, Approx. 605 p. 10 illus., Hardcover
ISBN: 0-8176-4471-7

About this book

This volume of invited articles by several outstanding mathematicians in algebra, algebraic geometry, and number theory is dedicated to Vladimir Drinfeld on the occasion of his 50th birthday. These surveys and original research articles broadly reflect the range of Drinfeld's work in these areas, especially his profound contributions to the Langlands program and mathematical physics.

Contributors include: V.V. Fock, E. Frenkel, D. Gaitsgory, A.B. Goncharov, E. Hrushovski, Y. Ihara, D. Kazhdan, M. Kisin, I. Krichever, G. Laumon, Yu. Manin, and V. Schechtmann.

Written for:

Graduate students, researchers, mathematicians, math physicists, algebraists, algebraic geometers, number theorists, students and colleagues of Drinfeld who know the impact of his work throughout the mathematical community

Table of contents

Preface
V. V. Fock and A.B. Goncharov: Cluster X-varieties, Amalgamation and Poisson?Lie Groups
E. Frenkel and D. Gaitsgory: Local Geometric Langlands Correspondence and Affine Kac?Moody Algebras
Y. Ihara: On the Euler?Kronecker Constants of Global Fields and Primes with Small Norm (includes appendix by M. Tsfasman)
D. Kazhdan and E. Hrushovski: Integration in Valued Fields
M. Kisin: Crystalline Representations and F-crystals
I. Krichever: Integrable Linear Equations and the Riemann?Schottky Problem
G. Laumon: Fibres de Springer et Jacobiennes Compactifiees
Yu. Manin: Iterated Integrals of Modular Forms and Noncommutative Modular Symbols
V. Schechtmann: Structures Membranaires

Ponnusamy, S., Silverman, Herb

Complex Variables with Applications

2006, Approx. 495 p. 109 illus., Hardcover
ISBN: 0-8176-4457-1

About this textbook

Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector. Exploited properly, each perspective provides crucial insight into the interrelations between the complex number system and its parent, the real number system. The authors explore these relationships by adopting both generalization and specialization methods to move from real variables to complex variables, and vice versa, while simultaneously examining their analytic and geometric characteristics, using geometry to illustrate analytic concepts and employing analysis to unravel geometric notions.

The engaging exposition is replete with discussions, remarks, questions, and exercises, motivating not only understanding on the part of the reader, but also developing the tools needed to think critically about mathematical problems. This focus involves a careful examination of the methods and assumptions underlying various alternative routes that lead to the same destination.

The material includes numerous examples and applications relevant to engineering students, along with some techniques to evaluate various types of integrals. The book may serve as a text for an undergraduate course in complex variables designed for scientists and engineers or for mathematics majors interested in further pursuing the general theory of complex analysis. The only prerequistite is a basic knowledge of advanced calculus. The presentation is also ideally suited for self-study.

Table of contents

Preface.- Algebraic and Geometric Preliminaries.- Topological and Analytic Preliminaries.- Bilinear Transformations and Mappings.- Elementary Functions.- Analytic Functions.- Power Series.- Complex Integration and Cauchy's Theorem.- Applications of Cauchy's Theorem.- Laurent Series and the Residue Theorem.- Harmonic Functions.- Conformal Mapping and the Riemann Mapping Theorem.- Entire and Meromorphic Functions.- Analytic Continuation.- Applications.- References.- Index of Special Notations.- Hints for Selected Questions and Exercises.- Index.

Langer, Matthias; Luger, Annemarie; Woracek, Harald (Eds.)

Operator Theory and Indefinite Inner Product Spaces

Series: Operator Theory: Advances and Applications, Vol. 163
2006, Approx. 410 p., Hardcover
ISBN: 3-7643-7515-9
A Birkhauser book

About this book

A colloquium on operator theory was held in Vienna, Austria, in March 2004, on the occasion of the retirement of Heinz Langer, a leading expert in operator theory and indefinite inner product spaces. The book contains fifteen refereed articles reporting on recent and original results in various areas of operator theory, all of them related with the work of Heinz Langer. The topics range from abstract spectral theory in Krein spaces to more concrete applications, such as boundary value problems, the study of orthogonal functions, or moment problems. The book closes with a historical survey paper.

Table of contents

Preface.- Laudatory Speech.- Speech of Heinz Langer.- Conference Programme.- List of Participants.- Bibliography of Heinz Langer.- Contributions by M. Adamyan, Y. Arlinski, J. Behrndt, P. Binding, B. Curgus, A. Dijksma, A. Fleige, K.-H. Forster, B. Fritsche, S. Hassi, M. Kaltenback, B. Kirstein, P. Lancaster, A. Lasarow, A. Luger, L.V. Mikaelyan, B. Nagy, D. Popovici, U. Prells, Sasvari, J. Shondin, H. de Snoo, V. Strauss, F.H. Szafraniec, B. Textorius, I.M. Tkachenko, H. Winkler, H. Woracek.

Boggiatto, P.; Rodino, L.; Toft, J.; Wong, M.W. (Eds.)

Pseudo-Differential Operators and Related Topics

Series: Operator Theory: Advances and Applications, Vol. 164
2006, Approx. 255 p., Hardcover
ISBN: 3-7643-7513-2

About this book

This volume contains articles based on lectures given at the International Conference on Pseudo-differential Operators and Related Topics at Vaxjo University in Sweden from June 22 to June 25, 2005. Sixteen refereed articles by experts from Canada, Denmark, England, Italy, Japan, Mexico, Russia, Serbia and Montenegro, and Sweden are devoted to pseudo-differential operators and related topics. They cover a broad spectrum of topics such as partial differential equations, Wigner transforms, Weyl transforms on Euclidean spaces and Lie groups, mathematical physics, time-frequency analysis, frames and stochastic processes.

Table of contents

Preface.- Contributions by M.S. Agranovich, A. Ascanelli, M. Cappiello, O. Christensen, M. Cicognani, E. Cordero, K. Furutani, M. de Gosson, G. Garello, I. Kamotski, A. Khrennikov, F. De Mari, A. Morando, K. Nowak, V.S. Rabinovich, M. Ruzhanski, M. Sugimoto, A. Tabacco, N. Teofanov, J. Toft, P. Wahlberg, M.W. Wong, L. Zanghirati.

Kontsevich's Formula for Rational Plane Curves

An Invitation to Quantum Cohomology

Series: Progress in Mathematics, Vol. 249
Kock, Joachim, Vainsencher, Israel
2006, Approx. 175 p. 30 illus., Hardcover
ISBN: 0-8176-4456-3

About this book

This elementary introduction to stable maps and quantum cohomology presents the problem of counting rational plane curves mostly from the viewpoint of enumerative geometry. The preliminary material begins with an introduction to stable pointed curves and culminates with a proof of the associativity of the quantum product. Kontsevich's formula is initially established in the framework of classical enumerative geometry, then as a statement about reconstruction for Gromov?Witten invariants, and finally, using generating functions, as a special case of the associativity of the quantum product.

Emphasis is given throughout the exposition to examples, heuristic discussions, and simple applications of the basic tools to best convey the intuition behind the subject. The book demystifies these new quantum techniques by showing how they fit into classical algebraic geometry.

Some background in algebraic geometry, the basic notions of moduli spaces, elementary intersection theory, and Poincare duality is assumed. The book is ideal for self-study, as a text for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersection theory. The book will prove equally useful to graduate students in the classroom setting as to researchers, geometers, and physicists working in the field.

Table of contents

Preface.- Introduction.- Prologue: Warming Up with Cross-ratios, and the Definition of Moduli Space.- Stable n-pointed Curves.- Stable Maps.- Enumerative Geometry via Stable Maps.- Gromov?Witten Invariants.- Quantum Cohomology.- Bibliography.- Index.