Problems In The Classification Of E0 Semigroups
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Problems In The Classification Of E0 Semigroups
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Author : Masayasu Aotani
language : en
Publisher:
Release Date : 1996
Problems In The Classification Of E0 Semigroups written by Masayasu Aotani and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Noncommutative Dynamics And E Semigroups
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Author : William Arveson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-06
Noncommutative Dynamics And E Semigroups written by William Arveson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-06 with Mathematics categories.
These days, the term Noncommutative Dynamics has several interpretations. It is used in this book to refer to a set of phenomena associated with the dynamical evo lution of quantum systems of the simplest kind that involve rigorous mathematical structures associated with infinitely many degrees of freedom. The dynamics of such a system is represented by a one-parameter group of automorphisms of a non commutative algebra of observables, and we focus primarily on the most concrete case in which that algebra consists of all bounded operators on a Hilbert space. If one introduces a natural causal structure into such a dynamical system, then a pair of one-parameter semigroups of endomorphisms emerges, and it is useful to think of this pair as representing the past and future with respect to the given causality. These are both Eo-semigroups, and to a great extent the problem of understanding such causal dynamical systems reduces to the problem of under standing Eo-semigroups. The nature of these connections is discussed at length in Chapter 1. The rest of the book elaborates on what the author sees as the impor tant aspects of what has been learned about Eo-semigroups during the past fifteen years. Parts of the subject have evolved into a satisfactory theory with effective toolsj other parts remain quite mysterious. Like von Neumann algebras, Eo-semigroups divide naturally into three types: 1,11,111.
Classification Of E 0 Semigroups By Product Systems
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Author : Michael Skeide
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-03-10
Classification Of E 0 Semigroups By Product Systems written by Michael Skeide and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-10 with Mathematics categories.
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.
Advances In Quantum Dynamics
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Author : Geoffrey L. Price
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Advances In Quantum Dynamics written by Geoffrey L. Price and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
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.
The Abc Problem For Gabor Systems
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Author : Xin-Rong Dai
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-10-05
The Abc Problem For Gabor Systems written by Xin-Rong Dai and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-05 with Mathematics categories.
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.
Selected Papers On Probability And Statistics
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Selected Papers On Probability And Statistics written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
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.
Advances In The Theory Of Varieties Of Semigroups
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Author : Edmond W. H. Lee
language : en
Publisher: Springer Nature
Release Date : 2023-04-08
Advances In The Theory Of Varieties Of Semigroups written by Edmond W. H. Lee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-08 with Mathematics categories.
This monograph thoroughly explores the development of the theory of varieties of semigroups and of two related algebras: involution semigroups and monoids. Through this in-depth analysis, readers will attain a deeper understanding of the differences between these three types of varieties, which may otherwise seem counterintuitive. New results with detailed proofs are also presented that answer previously unsolved fundamental problems. Featuring both a comprehensive overview as well as highlighting the author’s own significant contributions to the area, this book will help establish this subfield as a matter of timely interest. Advances in the Theory of Varieties of Semigroups will appeal to researchers in universal algebra and will be particularly valuable for specialists in semigroups.
Operator Theory Operator Algebras And Applications
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Author : Deguang Han
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Operator Theory Operator Algebras And Applications written by Deguang Han and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
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.
Quantization Nonlinear Partial Differential Equations And Operator Algebra
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Author : William Arveson
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Quantization Nonlinear Partial Differential Equations And Operator Algebra written by William Arveson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
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.
Stochastic Cauchy Problems In Infinite Dimensions
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Author : Irina V. Melnikova
language : en
Publisher: CRC Press
Release Date : 2016-04-27
Stochastic Cauchy Problems In Infinite Dimensions written by Irina V. Melnikova and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-27 with Mathematics categories.
Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory. The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.