Kategoria BISAC: Mathematics >> Functional Analysis

The monograph is devoted to the study of functional equations with the transformed argument on the real line and on the unit circle. Such equations systematically arise in dynamical systems, differential equations, probabilities, singularities of smooth mappings, and other areas. The purpose of the book is to present modern methods and new results in the subject, with an emphasis on a connection between local and global solvability. The general concepts developed in the book are applicable to multidimensional functional equations. Some of the methods are presented for the first time in the...

This book presents nine survey articles addressing topics surrounding positivity, with an emphasis on functional analysis. The book assembles a wide spectrum of research into positivity, providing up-to-date information on topics of current interest. The discussion provides insight into classical areas like spaces of continuous functions, f-algebras, and integral operators. The coverage extends is broad, including vector measures, operator spaces, ordered tensor products, and non-commutative Banach function spaces.

A beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the other yields a uniform treatment of several kinds of Hamiltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes. For such operators regular and singular perturbations of order zero and their spectral properties are investigated.
A complete treatment of the Feynman-Kac formula is given. The theory is applied to such topics as compactness or trace class properties...

Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, the Handbook of mathematical functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over...

One of the beautiful results in the representation theory of the finite groups is McKay's theorem on a correspondence between representations of the binary polyhedral group of SU(2) and vertices of an extended simply-laced Dynkin diagram.

The Coxeter transformation is the main tool in the proof of the McKay correspondence, and is closely interrelated with the Cartan matrix and Poincare series. The Coxeter functors constructed by Bernstein, Gelfand and Ponomarev plays a distinguished role in the representation theory of quivers.

On these pages, the ideas and formulas due to...

This monograph systematically develops and considers the so-called "dressing method" for solving differential equations (both linear and nonlinear), a means to generate new non-trivial solutions for a given equation from the (perhaps trivial) solution of the same or related equation. Throughout, the text exploits the "linear experience" of presentation, with special attention given to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions.

This unique book is devoted to the detailed study of the recently discovered commutative C*-algebras of Toeplitz operators on the Bergman space over the unit disk. Surprisingly, the key point to understanding their structure and classifying them lies in the hyperbolic geometry of the unit disk. The book develops a number of important problems whose successful solution was made possible and is based on the specific features of the Toeplitz operators from these commutative algebras.

This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the conference "Algebraic Analysis of Differential Equations from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. This volume is dedicated to Professor Takahiro Kawai, who is one of the creators of microlocal analysis and who introduced the technique of microlocal analysis into exponential asymptotics.

This book contains a collection of recent research papers originating from the 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, which was held at the TU Berlin, Germany, December 14 to 17, 2006. The contributions in this volume are devoted to spectral and perturbation theory of linear operators in spaces with an inner product, generalized Nevanlinna functions and problems and applications in the field of differential equations. Among the discussed topics are linear relations, singular perturbations, de Branges spaces, nonnegative matrices and abstract kinetic...