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Algebras of Functions on Quantum Groups: Part I

1998 Mathematics
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Release : 1998
Genre : Mathematics
Kind : eBook
Book Rating : 360/5 ( reviews)

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Book Synopsis Algebras of Functions on Quantum Groups: Part I by : Leonid I. Korogodski

Download or read book Algebras of Functions on Quantum Groups: Part I written by Leonid I. Korogodski. This book was released on 1998. Available in PDF, EPUB and Kindle. Book excerpt: The text is devoted to the study of algebras of functions on quantum groups. The book includes the theory of Poisson-Lie algebras (quasi-classical version of algebras of functions on quantum groups), a description of representations of algebras of functions and the theory of quantum Weyl groups. It can serve as a text for an introduction to the theory of quantum groups and is intended for graduate students and research mathematicians working in algebra, representation theory and mathematical physics.

Amenability

1988 Mathematics
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Release : 1988
Genre : Mathematics
Kind : eBook
Book Rating : 857/5 ( reviews)

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Book Synopsis Amenability by : Alan L. T. Paterson

Download or read book Amenability written by Alan L. T. Paterson. This book was released on 1988. Available in PDF, EPUB and Kindle. Book excerpt: The subject of amenability has its roots in the work of Lebesgue at the turn of the century. In the 1940s, the subject began to shift from finitely additive measures to means. This shift is of fundamental importance, for it makes the substantial resources of functional analysis and abstract harmonic analysis available to the study of amenability. The ubiquity of amenability ideas and the depth of the mathematics involved points to the fundamental importance of the subject. This book presents a comprehensive and coherent account of amenability as it has been developed in the large and varied literature during this century. The book has a broad appeal, for it presents an account of the subject based on harmonic and functional analysis. In addition, the analytic techniques should be of considerable interest to analysts in all areas. In addition, the book contains applications of amenability to a number of areas: combinatorial group theory, semigroup theory, statistics, differential geometry, Lie groups, ergodic theory, cohomology, and operator algebras. The main objectives of the book are to provide an introduction to the subject as a whole and to go into many of its topics in some depth. The book begins with an informal, nontechnical account of amenability from its origins in the work of Lebesgue. The initial chapters establish the basic theory of amenability and provide a detailed treatment of invariant, finitely additive measures (i.e., invariant means) on locally compact groups. The author then discusses amenability for Lie groups, "almost invariant" properties of certain subsets of an amenable group, amenability and ergodic theorems, polynomial growth, and invariant mean cardinalities. Also included are detailed discussions of the two most important achievements in amenability in the 1980s: the solutions to von Neumann's conjecture and the Banach-Ruziewicz Problem. The main prerequisites for this book are a sound understanding of undergraduate-level mathematics and a knowledge of abstract harmonic analysis and functional analysis. The book is suitable for use in graduate courses, and the lists of problems in each chapter may be useful as student exercises.

Stochastic Partial Differential Equations

2017-07-06 Mathematics
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Release : 2017-07-06
Genre : Mathematics
Kind : eBook
Book Rating : 475/5 ( reviews)

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Book Synopsis Stochastic Partial Differential Equations by : Sergey V. Lototsky

Download or read book Stochastic Partial Differential Equations written by Sergey V. Lototsky. This book was released on 2017-07-06. Available in PDF, EPUB and Kindle. Book excerpt: Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected to the material discussed at a particular place in the text. The questions usually ask to verify something, so that the reader already knows the answer and, if pressed for time, can move on. Accordingly, no solutions are provided, but there are often hints on how to proceed. The book will be of interest to everybody working in the area of stochastic analysis, from beginning graduate students to experts in the field.

Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems

1995 Mathematics
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Release : 1995
Genre : Mathematics
Kind : eBook
Book Rating : 873/5 ( reviews)

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Book Synopsis Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems by : Hal L. Smith

Download or read book Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems written by Hal L. Smith. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt: This book presents comprehensive treatment of a rapidly developing area with many potential applications: the theory of monotone dynamical systems and the theory of competitive and cooperative differential equations. The primary aim is to provide potential users of the theory with techniques, results, and ideas useful in applications, while at the same time providing rigorous proofs. Among the topics discussed in the book are continuous-time monotone dynamical systems, and quasimonotone and nonquasimonotone delay differential equations. The book closes with a discussion of applications to quasimonotone systems of reaction-diffusion type. Throughout the book, applications of the theory to many mathematical models arising in biology are discussed. Requiring a background in dynamical systems at the level of a first graduate course, this book is useful to graduate students and researchers working in the theory of dynamical systems and its applications.

The Bieberbach Conjecture: Proceedings of the Symposium on the Occasion of the Proof

1986 Mathematics
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Release : 1986
Genre : Mathematics
Kind : eBook
Book Rating : 210/5 ( reviews)

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Book Synopsis The Bieberbach Conjecture: Proceedings of the Symposium on the Occasion of the Proof by : Albert Baernstein (II)

Download or read book The Bieberbach Conjecture: Proceedings of the Symposium on the Occasion of the Proof written by Albert Baernstein (II). This book was released on 1986. Available in PDF, EPUB and Kindle. Book excerpt: Louis de Branges of Purdue University is recognized as the mathematician who proved Bieberbach's conjecture. This book offers insight into the nature of the conjecture, its history and its proof. It is suitable for research mathematicians and analysts.

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