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
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
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.
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.
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.
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.