Download or read book Problems in the Classification of E0 semigroups written by Masayasu Aotani and published by . This book was released on 1996 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Noncommutative Dynamics and E Semigroups written by William Arveson and published by Springer Science & Business Media. This book was released on 2012-11-06 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the notion of an E-semigroup, a generalization of the known concept of E_O-semigroup. These objects are families of endomorphisms of a von Neumann algebra satisfying certain natural algebraic and continuity conditions. Its thorough approach is ideal for graduate students and research mathematicians.
Download or read book Classification of E 0 Semigroups by Product Systems written by Michael Skeide and published by American Mathematical Soc.. This book was released on 2016-03-10 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these notes the author presents a complete theory of classification of E0-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.
Download or read book Advances in Quantum Dynamics written by Geoffrey L. Price and published by American Mathematical Soc.. This book was released on 2003 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on Advances in Quantum Dynamics. The purpose of the conference was to assess the current state of knowledge and to outline future research directions of quantum dynamical semigroups on von Neumann algebras. Since the appearance of the landmark papers by F. Murray and J. von Neumann, On the Rings of Operators, von Neumann algebras have been used as a mathematical model in the study of time evolution of quantum mechanical systems.Following the work of M. H. Stone, von Neumann, and others on the structure of one-parameter groups of unitary transformations, many researchers have made fundamental contributions to the understanding of time-reversible dynamical systems. This book deals with the mathematics of time-irreversiblesystems, also called dissipative systems. The time parameter is the half-line, and the transformations are now endomorphisms as opposed to automorphisms. For over a decade, W. B. Arveson and R. T. Powers have pioneered the effort to understand the structure of irreversible quantum dynamical systems on von Neumann algebras. Their papers in this volume serve as an excellent introduction to the theory. Also included are contributions in other areas which have had an impact on the theory, such asBrownian motion, dilation theory, quantum probability, and free probability. The volume is suitable for graduate students and research mathematicians interested in the dynamics of quantum systems and corresponding topics in the theory of operator algebras.
Download or read book Selected Papers on Probability and Statistics written by and published by American Mathematical Soc.. This book was released on 2009 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains translations of papers that originally appeared in the Japanese journal Sugaku. The papers range over a variety of topics in probability theory, statistics, and applications. This volume is suitable for graduate students and research mathematicians interested in probability and statistics.
Download or read book Classification of E0 semigroups by Product Systems written by Michael Skeide and published by . This book was released on 2016 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operator Theory Operator Algebras and Applications written by Deguang Han and published by American Mathematical Soc.. This book was released on 2006 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a presentation of some new trends in operator theory and operator algebras, with a view to their applications. It consists of separate papers written by some of the leading practitioners in the field. The content is put together by the three editors in a way that should help students and working mathematicians in other parts of the mathematical sciences gain insight into an important part of modern mathematics and its applications. While different specialist authors are outlining new results in this book, the presentations have been made user friendly with the aid of tutorial material. In fact, each paper contains three things: a friendly introduction with motivation, tutorial material, and new research. The authors have strived to make their results relevant to the rest of mathematics. A list of topics discussed in the book includes wavelets, frames and their applications, quantum dynamics, multivariable operator theory, $C*$-algebras, and von Neumann algebras. Some longer papers present recent advances on particular, long-standing problems such as extensions and dilations, the Kadison-Singer conjecture, and diagonals of self-adjoint operators.
Download or read book Quantization Nonlinear Partial Differential Equations and Operator Algebra written by William Arveson and published by American Mathematical Soc.. This book was released on 1996 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the outstanding recent progress in this important and challenging field and presents general background for the scientific context and specifics regarding key difficulties. Quantization is developed in the context of rigorous nonlinear quantum field theory in four dimensions and in connection with symplectic manifold theory and random Schrödinger operators. Nonlinear wave equations are exposed in relation to recent important progress in general relativity, in purely mathematical terms of microlocal analysis, and as represented by progress on the relativistic Boltzmann equation. Most of the developments in this volume appear in book form for the first time. The resulting work is a concise and informative way to explore the field and the spectrum of methods available for its investigation.
Download or read book The abc Problem for Gabor Systems written by Xin-Rong Dai and published by American Mathematical Soc.. This book was released on 2016-10-05 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: A longstanding problem in Gabor theory is to identify time-frequency shifting lattices aZ×bZ and ideal window functions χI on intervals I of length c such that {e−2πinbtχI(t−ma): (m,n)∈Z×Z} are Gabor frames for the space of all square-integrable functions on the real line. In this paper, the authors create a time-domain approach for Gabor frames, introduce novel techniques involving invariant sets of non-contractive and non-measure-preserving transformations on the line, and provide a complete answer to the above abc-problem for Gabor systems.
Download or read book An Inverse Spectral Problem Related to the Geng Xue Two Component Peakon Equation written by Hans Lundmark and published by American Mathematical Soc.. This book was released on 2016-10-05 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors solve a spectral and an inverse spectral problem arising in the computation of peakon solutions to the two-component PDE derived by Geng and Xue as a generalization of the Novikov and Degasperis-Procesi equations. Like the spectral problems for those equations, this one is of a ``discrete cubic string'' type-a nonselfadjoint generalization of a classical inhomogeneous string--but presents some interesting novel features: there are two Lax pairs, both of which contribute to the correct complete spectral data, and the solution to the inverse problem can be expressed using quantities related to Cauchy biorthogonal polynomials with two different spectral measures. The latter extends the range of previous applications of Cauchy biorthogonal polynomials to peakons, which featured either two identical, or two closely related, measures. The method used to solve the spectral problem hinges on the hidden presence of oscillatory kernels of Gantmacher-Krein type, implying that the spectrum of the boundary value problem is positive and simple. The inverse spectral problem is solved by a method which generalizes, to a nonselfadjoint case, M. G. Krein's solution of the inverse problem for the Stieltjes string.
Download or read book Continuous Analogues of Fock Space written by William Arveson and published by American Mathematical Soc.. This book was released on 1989 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of classifying semigroups of endomorphisms of type [italic]I[subscript]infinity symbol factors to outer conjugacy is reduced to the problem of classifying certain simpler structures associated to them, called product systems. Product systems are intimately connected with continuous tensor products of Hilbert spaces. We develop the general theory of product systems and give a number of applications to semigroups of endomorphisms of von Neumann algebras; in particular, we introduce a numerical invariant for such semigroups which is analogous to the Fredholm index.
Download or read book Parallel Computing Using the Prefix Problem written by S. Lakshmivarahan and published by Oxford University Press on Demand. This book was released on 1994 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to those aspects of parallel programming and parallel algorithms that relate to a single topic: the prefix problem. This approach provides intense development of a single computational tool used in many parallel computations, showing and discussing its techniques. The text may be used for graduate courses.
Download or read book Proceedings of Symposia in Pure Mathematics written by and published by . This book was released on 1990 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cocycles of CCR Flows written by B. V. Rajarama Bhat and published by American Mathematical Soc.. This book was released on 2001 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the partially ordered set of quantum dynamical semigroups dominated by a given semigroup on the algebra of all bounded operators on a Hilbert space. For semigroups of *-endomorphisms this set can be described through cocycles. This helps us to prove a factorization theorem for dilations and to show that minimal dilations of quantum dynamical semigroups with bounded generators can be got through Hudson-Parthasarathy cocycles.
Download or read book Classical Finite Transformation Semigroups written by Olexandr Ganyushkin and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, cross-sections and variants. The book contains many exercises and historical comments and is directed first of all to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but also to tutors and researchers.
Download or read book Stochastic PDE s and Kolmogorov Equations in Infinite Dimensions written by N.V. Krylov and published by Springer. This book was released on 2006-11-15 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finite-dimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LP-analysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results.
Download or read book Operator Theory written by William Arveson and published by . This book was released on 1990 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt:
