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Introduction to Matrix Analysis and Applications
Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.
Contributions to Operator Theory and its Applications
This volume is dedicated to Tsuyoshi Ando, a foremost expert in operator theory, matrix theory, complex analysis, and their applications, on the occasion of his 60th birthday. The book opens with his biography and list of publications. It contains a selection of papers covering a broad spectrum of topics ranging from abstract operator theory to various concrete problems and applications. The majority of the papers deal with topics in modern operator theory and its applications. This volume also contains papers on interpolation and completion problems, factorization problems and problems connected with complex analysis. The book will appeal to a wide audience of pure and applied mathematicians.
Large Deviations for Stochastic Processes
The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are derived for a class of Hamilton-Jacobi equations in Hilbert spaces and in spaces of probability measures.
Advances in Differential Equations and Mathematical Physics
The text offers a combination of certain emerging topics and important research advances in the area of differential equations. The topics range widely and include magnetic Schroedinger operators, the Boltzmann equations, nonlinear variational problems and noncommutative probability theory. The text is suitable for graduate and advanced graduate courses and seminars on the topic, as well as research mathematicians and physicists working in mathematical physics, applied mathematics, analysis and differential equations.
Sturm-Liouville Theory
In 1836-1837 Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which started the subject now known as the Sturm-Liouville problem. In 1910 Hermann Weyl published an article which started the study of singular Sturm-Liouville problems. Since then, the Sturm-Liouville theory remains an intensely active field of research, with many applications in mathematics and mathematical physics. The purpose of the present book is (a) to provide a modern survey of some of the basic properties of Sturm-Liouville theory and (b) to bring the reader to the forefront of knowledge about some aspects of this theory. To use the book, only a basic knowledge of ...
Topology of Closed One-Forms
Farber examines the geometrical, topological, and dynamical properties of closed one-forms, highlighting the relations between their global and local features. He describes the Novikov numbers and inequalities, the universal complex and its construction, Bott-type inequalities and those with Von Neumann Betti numbers, equivariant theory, the exactness of Novikov inequalities, the Morse theory of harmonic forms, and Lusternick-Schnirelman theory. Annotation : 2004 Book News, Inc., Portland, OR (booknews.com).
Quantum Information Theory
This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of whic...
Selected Papers of M. Ohya
This volume is a collection of articles written by Professor M Ohya over the past three decades in the areas of quantum teleportation, quantum information theory, quantum computer, etc. By compiling Ohya''s important works in these areas, the book serves as a useful reference for researchers who are working in these fields. Sample Chapter(s). Introduction (109 KB). Chapter 1: Adaptive Dynamics and Its Applications To Chaos and Npc Problem (1,633 KB). Contents: Adaptive Dynamics and Its Applications; A Stochastic Limit Approach to the SAT Problem; Quantum Algorithm for SAT Problem and Quantum Mutual Entropy; NP Problem in Quantum Algorithm; New Quantum Algorithm for Studying NP-complete Probl...
Analysis and Operator Theory
Dedicated to Tosio Kato’s 100th birthday, this book contains research and survey papers on a broad spectrum of methods, theories, and problems in mathematics and mathematical physics. Survey papers and in-depth technical papers emphasize linear and nonlinear analysis, operator theory, partial differential equations, and functional analysis including nonlinear evolution equations, the Korteweg–de Vries equation, the Navier–Stokes equation, and perturbation theory of linear operators. The Kato inequality, the Kato type matrix limit theorem, the Howland–Kato commutator problem, the Kato-class of potentials, and the Trotter–Kato product formulae are discussed and analyzed. Graduate students, research mathematicians, and applied scientists will find that this book provides comprehensive insight into the significance of Tosio Kato’s impact to research in analysis and operator theory.
Modules over Non-Noetherian Domains
In this book, the authors present both traditional and modern discoveries in the subject area, concentrating on advanced aspects of the topic. Existing material is studied in detail, including finitely generated modules, projective and injective modules, and the theory of torsion and torsion-free modules. Some topics are treated from a new point of view. Also included are areas not found in current texts, for example, pure-injectivity, divisible modules, uniserial modules, etc. Special emphasis is given to results that are valid over arbitrary domains. The authors concentrate on modules over valuation and Prüfer domains, but also discuss Krull and Matlis domains, h-local, reflexive, and coherent domains. The volume can serve as a standard reference book for specialists working in the area and also is a suitable text for advanced-graduate algebra courses and seminars.
