Hardback
Series: Cambridge Tracts in Mathematics (No. 188)
ISBN: 9781107010512
4 b/w illus. 65 exercises
Dimensions: 228 x 152 mm
available from August 2011
One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics.
Introduction
1. Background
2. The operator-valued Poisson kernel and its applications
3. Properties (An,m) and factorization of integrable functions
4. Polynomially bounded operators with rich spectrum
5. Beurling algebras
6. Applications of a fixed-point theorem
7. Minimal vectors
8. Universal operators
9. Moment sequences and binomial sums
10. Positive and strictly-singular operators
Bibliography
Index.
Hardback
Series: London Mathematical Society Student Texts (No. 79)
ISBN: 9780521519632
ISBN: 9780521740227 (paperback)
90 b/w illus.
Dimensions: 228 x 152 mm
available from October 2011
Few books on the subject of Riemann surfaces cover the relatively modern theory of dessins d'enfants (children's drawings), which was launched by Grothendieck in the 1980s and is now an active field of research. In this book, the authors begin with an elementary account of the theory of compact Riemann surfaces viewed as algebraic curves and as quotients of the hyperbolic plane by the action of Fuchsian groups of finite type. They then use this knowledge to introduce the reader to the theory of dessins d'enfants and its connection with algebraic curves defined over number fields. A large number of worked examples are provided to aid understanding, so no experience beyond the undergraduate level is required. Readers without any previous knowledge of the field of dessins d'enfants are taken rapidly to the forefront of current research.
1. Riemann surfaces and algebraic curves
2. Riemann surfaces and Fuchsian groups
3. Belyi's theorem
4. Dessins d'enfants
References
Index.
ISBN: 9781575866116
Publish July 2011 Paper
ISBN: 9781575866109
Published July 2011
220 pages | 6 x 9
Center for the Study of Language and Information - Lecture Notes
This book is a collection of papers on language processing, usage, and grammar, written to commemorate the career of Thomas Wasow on the occasion of his sixty-fifth birthday. Wasow has been professor of linguistics and philosophy at Stanford University since 1973, and is affiliated with the Symbolic Systems Program. He has made significant contributions to the study of English syntax, psycholinguistics, and philosophy of linguistics.
Cloth
ISBN: 9781575866314
Paper
ISBN: 9781575866307
Will Publish September 2011
254 pages | 6 x 9
This compilation of cutting-edge philosophical and scientific research comprises a survey of recent neuroscientific research on representational systems in animals and humans. Representational systems provide their owners with useful information about their environment and are shaped by the special informational needs of the organism with respect to its environment. In this volume, the authors address the long-standing dispute about the usefulness of the notion of representation in the study of behavior systems and offer a fresh perspective on representational systems that combines philosophical insights and experimental experience.
Cloth
ISBN: 9780226511788
384 pages | 6 x 9 | c 2012
Chicago Lectures in Mathematics
With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the localization and completion of topological spaces, model categories, and Hopf algebras.
The first half of the book sets out the basic theory of localization and completion of nilpotent spaces, using the most elementary treatment the authors know of. It makes no use of simplicial techniques or model categories, and it provides full details of other necessary preliminaries. With these topics as motivation, most of the second half of the book sets out the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and homological algebra are treated in parallel. A short last part develops the basic theory of bialgebras and Hopf algebras.