Series: Graduate Texts in Mathematics, Vol. 259
2011, XXX, 467 p. 104 illus., 52 in color., Hardcover
ISBN: 978-0-85729-020-5
Due: September 29, 2010
This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence.
Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits.
Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.
Motivation.- Ergodicity, Recurrence and Mixing.- Continued Fractions.- Invariant Measures for Continuous Maps.- Conditional Measures and Algebras.- Factors and Joinings.- Furstenberg’s Proof of Szemeredi’s Theorem.- Actions of Locally Compact Groups.- Geodesic Flow on Quotients of the Hyperbolic Plane.- Nilrotation.- More Dynamics on Quotients of the Hyperbolic Plane.- Appendix A: Measure Theory.- Appendix B: Functional Analysis.- Appendix C: Topological Groups
Series: Lecture Notes in Mathematics, Vol. 2006
Subseries: Seminaire de Probabilites2
011, X, 490 p. 28 illus., 14 in color.
ISBN: 978-3-642-15216-0
Due: November 2010
This is a new volume of the Seminaire de Probabilite which was started in the 60's. Following the tradition, this volume contains up to 20 original research and survey articles on several topics related to stochastic analysisThis volume contains J. Picard's advanced course on the representation formulae for the fractional Brownian motion. The regular chapters cover a wide range of themes, such as stochastic calculus and stochastic differential equations, stochastic differential geometry, filtrations, analysis of Wiener space, random matrices and free probability, as well as mathematical finance. Some of the contributions were presented at the Journees de Probabilites held in Poitiers in June 2009.
Series: Lecture Notes in Mathematics, Vol. 2008
2011, X, 294 p., Softcover
ISBN: 978-3-642-15707-3
Due: October 31, 2010
This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.
K-theory for group C*-algebras.- Universal Coefficient Theorems and assembly maps in KK-theory.- Algebraic v. topological K-theory: a friendly match.- Higher algebraic K-theory (after Quillen, Thomason and others).- Lectures on DG-categories
Series: Universitext
2011, XXX, 157 p. 220 illus., 110 in color., Softcover
ISBN: 978-0-85729-072-4
Due: November 27, 2010
During the past thirty years, strong relationships have interwoven the fields of dynamical systems, linear algebra and number theory. This rapport between different areas of mathematics has enabled the resolution of some important conjectures and has in fact given birth to new ones. This book sheds light on these relationships and their applications in an elementary setting, by showing that the study of curves on a surface can lead to orbits of a linear group or even to continued fraction expansions of real numbers.
Geodesic and Horocyclic Trajectories presents an introduction to the topological dynamics of two classical flows associated with surfaces of curvature ?1, namely the geodesic and horocycle flows. Written primarily with the idea of highlighting, in a relatively elementary framework, the existence of gateways between some mathematical fields, and the advantages of using them, historical aspects of this field are not addressed and most of the references are reserved until the end of each chapter in the Comments section. Topics within the text cover geometry, and examples, of Fuchsian groups; topological dynamics of the geodesic flow; Schottky groups; the Lorentzian point of view and Trajectories and Diophantine approximations.
This book will appeal to those with a basic knowledge of differential geometry including graduate students and experts with a general interest in the area
Dynamics of Fuchsian groups.- Examples of Fuchsian Groups.- Topological dynamics of the geodesic flow.- Schottky groups.- Topological dynamics.- The Lorentzian point of view.- Trajectories and Diophantine approximations.
Series: CMS Books in Mathematics
2011, XIV, 646 p. 40 illus., Hardcover
ISBN: 978-1-4419-7514-0
Due: November 29, 2010
Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics.
This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodym property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.
Preface.- Basic Concepts in Banach Spaces.- Hahn-Banach and Banach Open Mapping Theorems.- Weak Topologies and Banach Spaces.- Schauder Bases.- Structure of Banach Spaces.- Finite-Dimensional Spaces.- Optimization.- C^1 Smoothness in Separable Spaces.- Superreflexive Spaces.- Higher Order Smoothness.- Dentability and differentiability.- Basics in Nonlinear Geometric Analysis.- Weakly Compactly Generated Spaces.- Topics in Weak Topologies on Banach Spaces.- Compact Operators on Banach Spaces.- Tensor Products.- Appendix.- References.- Symbol Index.- Subject Index.- Author Index.