Dijksma, A., University of Groningen, The Netherlands,
Kaashoek, M.A., Ran, A.C.M., Vrije Universiteit, Amsterdam, The Netherlands, (Eds.)
Recent Advances in Operator Theory
The Israel Gohberg Anniversary Volume : International Workshop in Groningen, June 1998
Operator Theory: Advances and Applications vol.124
2001. Approx. 508 pages. Hardcover
ISBN 3-7643-6573-0
English
Due in June 2001
This book contains 25 papers, most of which were presented, for the first time, at the International Workshop on Operator Theory and its Applications held in Groningen, the Netherlands, from June 30-July 3, 1998. The topics include dilation and interpolation problems, reproducing kernel spaces, numerical ranges of operators, Riccati equations, harmonic analysis, spectral theory of differential operators and analytic operator functions to scattering of waves. All papers deal with operators in Banach or Hilbert spaces, or in spaces with an indefinite metric.
This volume is dedicated to Israel Gohberg, one of the founding fathers of the IWOTA worskhops and an outstanding leader in operator theory. His work had a deep influence on the field and its range of applications. The IWOTA Groningen 1998, the tenth in its series, was a good occasion for a pre-celebration of his 70th birthday. This book also contains the speeches held at the workshop dinner, a review of Israel Gohberg's contributions to mathematics and a complete list of his publications.
Aguade, J., Broto, C., Casacuberta, C., Universitat Autonoma de Barcelona, Bellaterra, Spain,
Cohomological Methods in Homotopy Theory
Barcelona Conference on Algebraic Topology, Bellaterra, Spain, June 4-10, 1998
Progress in Mathematics vol.196.
2001. Approx. 408 pages. Hardcover
ISBN 3-7643-6588-9
English
Due in June 2001
This book contains a collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. A call for articles was made on the occasion of an emphasis semester organized by the Centre de Recerca Matematica in Bellaterra (Barcelona) in 1998. The main topics treated in the book include abstract features of stable and unstable homotopy, homotopical localizations, p-compact groups, H-spaces, classifying spaces for proper actions, cohomology of discrete groups, K-theory and other generalized cohomology theories, configuration spaces, and Lusternik-Schnirelmann category.
The book is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory. New research directions in topology are highlighted. Moreover, this informative and educational book serves as a welcome reference for many new results and recent methods.
Pikulin, V., Moscow Power Engineering Institute, Russia,
Pohozaev, S., Steklov Institute of Mathematics, Moscow, Russia
Equations in Mathematical Physics
A practical course
2001. Approx. 216 pages. Hardcover
ISBN 3-7643-6501-3
English
Due in July 2001
Many physical processes in fields such as mechanics, thermodynamics, electricity, magnetism or optics are described by means of partial differential equations. The aim of the present book is to demontstrate the basic methods for solving the classical linear problems in mathematical physics of elliptic, parabolic and hyperbolic type. In particular, the methods of conformal mappings, Fourier analysis and Green's functions are considered, as well as the perturbation method and integral transformation method, among others. Every chapter contains concrete examples with a detailed analysis of their solution.
The book is intended as a textbook for students in mathematical physics, but will also serve as a handbook for scientists and engineers.
Timmesfeld, F.G., University of Giessen, Germany
Abstract Root Subgroups and Simple Groups of Lie-Type
Monographs in Mathematics 95
2001. Approx. 400 pages. Hardcover
ISBN 3-7643-6532-3
English
Due in July 2001
The present book is the first to systematically treat the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. For finite groups, this theory has been developed in the 1970s mainly by M. Aschbacher, B. Fischer and the author. It was extended to arbitrary groups in the 1990s by the author.
The theory of abstract root subgroups is an important tool to study and classify simple classical and Lie-type groups. It is strongly related to the theory of root groups on buildings developed by J. Tits, which in turn extends the theory of root subgroups of Chevalley groups.
The book is of interest to mathematicians working in different areas such as finite group theory, classsical groups, algebraic and Lie-type groups, buildings and generalized polygons. It will also be welcomed by the graduate student in any of the above subjects, as well as the researcher working in any of these areas. Parts of it can also be used for graduate classes. Large parts of the book are self-contained and accessible with reasonable knowledge in abstract group theory and classical groups. Its main purpose is to give complete and partially new proofs of results that are quite unaccessible in the literature.
Triebel, H., University of Jena, Germany
The Structure of Functions
Monographs in Mathematics97
2001. Approx. 440 pages. Hardcover
ISBN 3-7643-6546-3
English
Due in July 2001
This book deals with the constructive Weierstrassian approach to the theory of function spaces and various applications. The first chapter is devoted to a detailed study of quarkonial (subatomic) decompositions of functions and distributions on euclidean spaces, domains, manifolds and fractals. This approach combines the advantages of atomic and wavelet representations. It paves the way to sharp inqualities and embeddings in function spaces, spectral theory of fractal elliptic operators, and a regularity theory of some semi-linear equations.
The book is self-contained, although some parts may be considered as a continuation of the author's book Fractals and Spectra . It is directed to mathematicians and (theoretical) physicists interested in the topics indicated and, in particular, how they are interrelated.
Cherix, P.-A., Universite de Geneve, Switzerland
Cowling, M., University of New South Wales, Sydney, Australia
Jolissaint, P., Universite de Neuchatel, Switzerland, Julg, P., Universite dOrleans, France Valette, A., Universite de Neuchatel, Switzerland
Groups with the Haagerup Property
Gromov's a-T-menability
Progress in Mathematics 197
2001. Approx. 136 pages. Hardcover
ISBN 3-7643-6598-6
English
Due in August 2001
A locally compact group has the Haagerup property, or is a-T-menable in the sense of Gromov, if it admits a proper isometric action on some affine Hilbert space. As Gromov's pun is trying to indicate, this definition is designed as a strong negation to Kazhdan's property (T), characterized by the fact that every isometric action on some affine Hilbert space has a fixed point.
The class of a-T-menable groups is remarkably large, containing amenable groups, free groups (more generally groups acting properly on trees), Coxeter groups, closed subgroups of isometries of real or complex hyperbolic spaces, and much more.
Although the Haagerup property was originally introduced in functional and harmonic analysis as an approximation property of certain operator algebras, it was gradually realised that this property was actually of geometric nature. So its study leads into various areas of mathematics, such as geometric group theory, ergodic theory, representation theory of Lie groups, and operator algebras. (The latter enter in particular via the celebrated Baum-Connes conjecture; it is a remarkable result by Higson and Kasparov that the class of a-T-menable groups satisfy the Baum-Connes conjecture.)
The aim of this book is to cover, for the first time in book form, various aspects of the Haagerup property. New characterisations are brought in, using ergodic theory or operator algebras. Several new examples are given, and new approaches to previously known examples are proposed. Connected Lie groups with the Haagerup property are completely characterized.
The book, which ends with a list of open questions, will be of interest to graduate students and researchers in the fields of geometry, group theory, harmonic analysis, ergodic theory, and operator algebras.