Download or read book Product Formulas Nonlinear Semigroups and Addition of Unbounded Operators written by Paul R. Chernoff and published by American Mathematical Soc.. This book was released on 1974 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work deals with the general theory, both linear and non-linear, of operator semigroup product formulas of the type lim [over] n[right arrow][infinity] F(t/n) [superscript]n = G(t). The principal application is the use of the Trotter-Lie product formula e [superscript]tC = lim [over] n[right arrow][infinity] (e [superscript]t/nA e [superscript]t/nB) [superscript]n to define a generalized addition of semigroup generators, and self-adjoint operators in particular. The properties of generalized addition, both regular and pathological, are discussed.
Download or read book Semigroups of Operators and Spectral Theory written by S Kantorovitz and published by CRC Press. This book was released on 1995-06-19 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some aspects of the theory of semigroups of operators, mostly from the point of view of its interaction withspectral theory. In order to make it self-contained, a concise description of the basic theory of semigroups, with complete proofs, is included in Part I. Some of the author's recent results, such as the construction of the Hille-Yosida space for general operators, the semi-simplicity manifold, and a Taylor formula for semigroups as functions of their generator, are also included in Part I. Part II describes recent generalizations (most of them in bookform for the first time), including pre-semigroups, semi-simplicity manifolds in situations more general than that considered in Part I, semigroups of unbounded symmetric operators, and an analogous result on "local cosine families" and semi-analytic vectors. It is hoped that this book will inspire more research in this field. This book will be of particular interest to graduate students and researchers working operator theory and its applications.
Download or read book Trotter Kato Product Formul written by Valentin A. Zagrebnov and published by Springer Nature. This book was released on with total page 879 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Semigroups of Linear Operators and Applications written by Jerome A. Goldstein and published by Courier Dover Publications. This book was released on 2017-05-17 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced graduate-level treatment of semigroup theory explores semigroups of linear operators and linear Cauchy problems. The text features challenging exercises and emphasizes motivation, heuristics, and further applications. 1985 edition.
Download or read book Semigroups of Operators Theory and Applications written by Jacek Banasiak and published by Springer Nature. This book was released on 2020-06-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features selected and peer-reviewed lectures presented at the 3rd Semigroups of Operators: Theory and Applications Conference, held in Kazimierz Dolny, Poland, in October 2018 to mark the 85th birthday of Jan Kisyński. Held every five years, the conference offers a forum for mathematicians using semigroup theory to discover what is happening outside their particular field of research and helps establish new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The book is intended for researchers, postgraduate and senior students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimisation and optimal control. The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while Hille and Yosida’s fundamental generation theorem dates back to the forties. The theory was originally designed as a universal language for partial differential equations and stochastic processes but, at the same time, it started to become an independent branch of operator theory. Today, it still has the same distinctive character: it develops rapidly by posing new ‘internal’ questions and, in answering them, discovering new methods that can be used in applications. On the other hand, it is being influenced by questions from PDE’s and stochastic processes as well as from applied sciences such as mathematical biology and optimal control and, as a result, it continually gathers new momentum. However, many results, both from semigroup theory itself and the applied sciences, are phrased in discipline-specific languages and are hardly known to the broader community.
Download or read book Counterexamples in Operator Theory written by Mohammed Hichem Mortad and published by Springer Nature. This book was released on 2022-05-03 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is the first of its kind exclusively devoted to counterexamples in operator theory and includes over 500 problems on bounded and unbounded linear operators in Hilbert spaces. This volume is geared towards graduate students studying operator theory, and the author has designated the difficulty level for each counterexample, indicating which ones are also suitable for advanced undergraduate students. The first half of the book focuses on bounded linear operators, including counterexamples in the areas of operator topologies, matrices of bounded operators, square roots, the spectrum, operator exponentials, and non-normal operators. The second part of the book is devoted to unbounded linear operators in areas such as closedness and closability, self-adjointness, normality, commutativity, and the spectrum, concluding with a chapter that features some open problems. Chapters begin with a brief “Basics” section for the readers’ reference, and many of the counterexamples included are the author’s original work. Counterexamples in Operator Theory can be used by students in graduate courses on operator theory and advanced matrix theory. Previous coursework in advanced linear algebra, operator theory, and functional analysis is assumed. Researchers, quantum physicists, and undergraduate students studying functional analysis and operator theory will also find this book to be a useful reference.
Download or read book Operator Theory Analysis and Mathematical Physics written by Jan Janas and published by Springer Science & Business Media. This book was released on 2007-04-29 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures delivered at the International Conference Operator Theory and its Applications in Mathematical Physics (OTAMP 2004), held at the Mathematical Research and Conference Center in Bedlewo near Poznan, Poland. The idea behind these lectures was to present interesting ramifications of operator methods in current research of mathematical physics.
Download or read book Operator Algebras and Quantum Statistical Mechanics 1 written by Ola Bratteli and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission ofvarious interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems of field theory and statistical mechanics. But the theory of 20 years aga was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.
Download or read book Nonlinear Evolution Equations written by Michael G. Crandall and published by Elsevier. This book was released on 2014-05-10 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Evolution Equation covers the proceedings of the Symposium by the same title, conducted by the Mathematics Research Center at the University of Wisconsin, Madison on October 17-19, 1977. This book is divided into 13 chapters and begins with reviews of the uniqueness of solution to systems of conservation laws and the computational aspects of Glimm's method. The next chapters examine the theoretical and practical aspects of Boltzmann, Navier-Stokes, and evolution equations. These topics are followed by discussions of the practical applications of Trotter's product formula for some nonlinear semigroups and the finite time blow-up in nonlinear problems. The closing chapters deal with a Hamiltonian approach to the K-dV and other equations, along with a variational method for finding periodic solutions of differential equations. This book will prove useful to mathematicians and engineers.
Download or read book The Cauchy Problem written by Hector O. Fattorini and published by Cambridge University Press. This book was released on 1983 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students.
Download or read book Indiana University Mathematics Journal written by and published by . This book was released on 1973 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operator Algebras and Quantum Statistical Mechanics written by Ola Bratteli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission of various interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems offield theory and statistical mechanics. But the theory of 20 years ago was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.
Download or read book Open Quantum Systems and Feynman Integrals written by P. Exner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every part of physics offers examples of non-stability phenomena, but probably nowhere are they so plentiful and worthy of study as in the realm of quantum theory. The present volume is devoted to this problem: we shall be concerned with open quantum systems, i.e. those that cannot be regarded as isolated from the rest of the physical universe. It is a natural framework in which non-stationary processes can be investigated. There are two main approaches to the treatment of open systems in quantum theory. In both the system under consideration is viewed as part of a larger system, assumed to be isolated in a reasonable approximation. They are differentiated mainly by the way in which the state Hilbert space of the open system is related to that of the isolated system - either by orthogonal sum or by tensor product. Though often applicable simultaneously to the same physical situation, these approaches are complementary in a sense and are adapted to different purposes. Here we shall be concerned with the first approach, which is suitable primarily for a description of decay processes, absorption, etc. The second approach is used mostly for the treatment of various relaxation phenomena. It is comparably better examined at present; in particular, the reader may consult a monograph by E. B. Davies.
Download or read book Michigan Mathematical Journal written by and published by . This book was released on 1972 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1884 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operator Algebras and Quantum Statistical Mechanics C and W algebras symmetry groups decomposition of states written by Ola Bratteli and published by Springer. This book was released on 1987 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book ESAIM written by and published by . This book was released on 2004 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt:
