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Author : Wolfgang Arendt
Publisher : Unknown
Page : 340 pages
File Size : 47,6 Mb
Release : 2007
Category : Operator theory
ISBN : UOM:39015073589700
Author : Abdo Abou Jaoudé
Publisher : Intechopen
Page : 0 pages
File Size : 51,8 Mb
Release : 2023-05
Category : Electronic
ISBN : 1838809929
Operator theory is a fascinating model that includes essential theorems and diverse applications in all science. This book discusses some fundamental aspects of pure and applied operator theory and the use of the theory to solve a large array of problems. As such, it will be of interest to scholars, researchers, and undergraduate and graduate students in pure and applied mathematics, classical and modern physics, engineering, and science in general.
Author : Arthur Frazho,Wisuwat Bhosri
Publisher : Springer Science & Business Media
Page : 430 pages
File Size : 49,6 Mb
Release : 2009-12-29
Category : Mathematics
ISBN : 9783034602921
In this monograph, we combine operator techniques with state space methods to solve factorization, spectral estimation, and interpolation problems arising in control and signal processing. We present both the theory and algorithms with some Matlab code to solve these problems. A classical approach to spectral factorization problems in control theory is based on Riccati equations arising in linear quadratic control theory and Kalman ?ltering. One advantage of this approach is that it readily leads to algorithms in the non-degenerate case. On the other hand, this approach does not easily generalize to the nonrational case, and it is not always transparent where the Riccati equations are coming from. Operator theory has developed some elegant methods to prove the existence of a solution to some of these factorization and spectral estimation problems in a very general setting. However, these techniques are in general not used to develop computational algorithms. In this monograph, we will use operator theory with state space methods to derive computational methods to solve factorization, sp- tral estimation, and interpolation problems. It is emphasized that our approach is geometric and the algorithms are obtained as a special application of the theory. We will present two methods for spectral factorization. One method derives al- rithms based on ?nite sections of a certain Toeplitz matrix. The other approach uses operator theory to develop the Riccati factorization method. Finally, we use isometric extension techniques to solve some interpolation problems.
Author : Tanja Eisner,Bálint Farkas,Markus Haase,Rainer Nagel
Publisher : Springer
Page : 628 pages
File Size : 46,7 Mb
Release : 2015-11-18
Category : Mathematics
ISBN : 9783319168982
Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. Topics include: • an intuitive introduction to ergodic theory • an introduction to the basic notions, constructions, and standard examples of topological dynamical systems • Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem • measure-preserving dynamical systems • von Neumann’s Mean Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem • strongly and weakly mixing systems • an examination of notions of isomorphism for measure-preserving systems • Markov operators, and the related concept of a factor of a measure preserving system • compact groups and semigroups, and a powerful tool in their study, the Jacobs–de Leeuw–Glicksberg decomposition • an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai,and Hindman, Furstenberg’s Correspondence Principle, theorems of Roth and Furstenberg–Sárközy) Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory
Author : Dorina Mitrea,Marius Mitrea
Publisher : American Mathematical Soc.
Page : 446 pages
File Size : 45,7 Mb
Release : 2008
Category : Differential equations, Partial
ISBN : 9780821844243
This volume contains a collection of papers contributed on the occasion of Mazya's 70th birthday by a distinguished group of experts of international stature in the fields of harmonic analysis, partial differential equations, function theory, and spectral analysis, reflecting the state of the art in these areas.
Author : George W. Hanson,Alexander B. Yakovlev
Publisher : Springer Science & Business Media
Page : 640 pages
File Size : 52,5 Mb
Release : 2013-03-09
Category : Science
ISBN : 9781475736793
This text discusses electromagnetics from the view of operator theory, in a manner more commonly seen in textbooks of quantum mechanics. It includes a self-contained introduction to operator theory, presenting definitions and theorems, plus proofs of the theorems when these are simple or enlightening.
Author : Nirmala Prakash
Publisher : World Scientific Publishing Company
Page : 864 pages
File Size : 43,5 Mb
Release : 2003-09-02
Category : Science
ISBN : 9781911298243
This book presents the basics of mathematics that are needed for learning the physics of today. It describes briefly the theories of groups and operators, finite- and infinite-dimensional algebras, concepts of symmetry and supersymmetry, and then delineates their relations to theories of relativity and black holes, classical and quantum physics, electroweak fields and Yang-Mills. It concludes with a chapter on (the complex theory of) strings and superstrings and their link to black holes — an idea that fascinates both the physicist and the mathematician. Contents:Complex Functions, Riemann Surfaces and Two-Dimensional Conformal Field Theory (an Introduction)Elements of Group Theory and Group RepresentationsA Primer on OperatorsBasics of Algebras and Related ConceptsInfinite-Dimensional AlgebrasThe Role of Symmetry in Physics and MathematicsAll That's Super — An IntroductionGravitation, Relativity and Black HolesBasics of Quantum TheoryTheory of Yang–Mills and the Yang–Mills–Higgs MechanismStrings and Superstrings (Elementary Aspects) Readership: Upper level undergraduates, graduate students, lecturers and researchers in theoretical physics, mathematical physics, quantum physics and astrophysics as well as Yang-Mills and superstring theory.
Author : Heinz H. Bauschke,Patrick L. Combettes
Publisher : Springer
Page : 624 pages
File Size : 40,7 Mb
Release : 2017-02-28
Category : Mathematics
ISBN : 9783319483115
This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated. Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada. Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.
Author : Florentin Smarandache
Publisher : Infinite Study
Page : 128 pages
File Size : 53,7 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9781599735313
This book is part of the book-series dedicated to the advances of neutrosophic theories and their applications, started by the author in 1998. Its aim is to present the last developments in the field. This is the second extended and improved edition of Neutrosophic Perspectives (September 2017; first edition was published in June 2017). For the first time, we now introduce: — Neutrosophic Duplets and the Neutrosophic Duplet Structures; — Neutrosophic Multisets (as an extension of the classical multisets); — Neutrosophic Spherical Numbers; — Neutrosophic Overnumbers / Undernumbers / Offnumbers; — Neutrosophic Indeterminacy of Second Type; — Neutrosophic Hybrid Operators (where the heterogeneous t-norms and t-conorms may be used in designing neutrosophic aggregations); — Neutrosophic Triplet Weak Set (and con-sequently we have renamed the previous Neutros-ophic Triplet Set (2014-2016) as Neutrosophic Triplet Strong Set in order to distinguish them); — Neutrosophic Perfect Triplet; — Neutrosophic Imperfect Triplet; — Neutrosophic triplet relation of equivalence; — Two Neutrosophic Friends; — n Neutrosophic Friends; — Neutrosophic Triplet Loop; — Neutrosophic Triplet Function; — Neutrosophic Modal Logic; — and Neutrosophic Hedge Algebras. The Refined Neutrosophic Set / Logic / Probability were introduced in 2013 by F. Smarandache. Since year 2016 a new interest has been manifested by researchers for the Neutrosophic Triplets and their corresponding Neutros-ophic Triplet Algebraic Structures (introduced by F. Smarandache & M. Ali). Subtraction and Division of Neutrosophic Numbers were introduced by F. Smarandache - 2016, and Jun Ye – 2017. We also present various new applications in: neutrosophic multi-criteria decision-making, neutrosophic psychology, neutrosophic geographical function (the equatorial virtual line), neutrosophic probability in target identification, neutrosophic dynamic systems, neutrosophic quantum computers, neutrosophic theory of evolution, and neutrosophic triplet structures in our everyday life. Keywords: neutrosophy, neutrosophic duplets, neutrosophic duplet structures, neutrosophic multisets, neutrosophic hedge algebras, neutrosophic multi-criteria decision-making, neutrosophic psychology, neutrosophic geographical function, neutrosophic probability in target identification,
Author : Emanuele Crisostomi,Bissan Ghaddar,Florian Häusler,Joe Naoum-Sawaya,Giovanni Russo,Robert Shorten
Publisher : Springer Nature
Page : 343 pages
File Size : 52,7 Mb
Release : 2020-03-11
Category : Technology & Engineering
ISBN : 9783030350321
The book provides an encompassing overview of all aspects relating to the sharing economy paradigm in different fields of study, and shows the ongoing research efforts in filling previously identified gaps in understanding in this area. Control and optimization analytics for the sharing economy explores bespoke analytics, tools, and business models that can be used to help design collaborative consumption services (the shared economy). It provides case studies of collaborative consumption in the areas of energy and mobility. The contributors review successful examples of sharing systems, and explore the theory for designing effective and stable shared-economy models. They discuss recent innovations in and uses of shared economy models in niche areas, such as energy and mobility. Readers learn the scientific challenging issues associated with the realization of a sharing economy. Conceptual and practical matters are examined, and the state-of-the-art tools and techniques to address such applications are explained. The contributors also show readers how topical problems in engineering, such as energy consumption in power grids, or bike sharing in transportation networks, can be formulated and solved from a general collaborative consumption perspective. Since the book takes a mathematical perspective to the topic, researchers in business, computer science, optimization and control find it useful. Practitioners also use the book as a point of reference, as it explores and investigates the analytics behind economy sharing.
Author : Felix A Buot
Publisher : World Scientific
Page : 594 pages
File Size : 53,8 Mb
Release : 2024-04-23
Category : Science
ISBN : 9789811264733
This book employs nonequilibrium quantum transport, based on the use of mixed Hilbert space representations and real time quantum superfield transport theory, to explain various topological phases of systems with entangled chiral degrees of freedom. It presents an entirely new perspective on topological systems, entanglement-induced localization and delocalization, integer quantum Hall effect (IQHE), fractional quantum Hall effect (FQHE), and its respective spectral zones in the Hofstadter butterfly spectrum. A simple and powerful, intuitive, and wide-ranging perspective on chiral transport dynamics.
Author : Richard M. Aron,Mohammad Sal Moslehian,Ilya M. Spitkovsky,Hugo J. Woerdeman
Publisher : Springer Nature
Page : 822 pages
File Size : 53,7 Mb
Release : 2022-08-10
Category : Mathematics
ISBN : 9783031021046
Inequalities play a central role in mathematics with various applications in other disciplines. The main goal of this contributed volume is to present several important matrix, operator, and norm inequalities in a systematic and self-contained fashion. Some powerful methods are used to provide significant mathematical inequalities in functional analysis, operator theory and numerous fields in recent decades. Some chapters are devoted to giving a series of new characterizations of operator monotone functions and some others explore inequalities connected to log-majorization, relative operator entropy, and the Ando-Hiai inequality. Several chapters are focused on Birkhoff–James orthogonality and approximate orthogonality in Banach spaces and operator algebras such as C*-algebras from historical perspectives to current development. A comprehensive account of the boundedness, compactness, and restrictions of Toeplitz operators can be found in the book. Furthermore, an overview of the Bishop-Phelps-Bollobás theorem is provided. The state-of-the-art of Hardy-Littlewood inequalities in sequence spaces is given. The chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.
Author : Jim Agler,John Edward McCarthy,Nicholas John Young
Publisher : Cambridge University Press
Page : 393 pages
File Size : 46,8 Mb
Release : 2020-03-26
Category : Mathematics
ISBN : 9781108485449
This monograph, aimed at graduate students and researchers, explores the use of Hilbert space methods in function theory. Explaining how operator theory interacts with function theory in one and several variables, the authors journey from an accessible explanation of the techniques to their uses in cutting edge research.
Author : Gerard A.J.M Jagers op Akkerhuis
Publisher : Springer
Page : 295 pages
File Size : 48,5 Mb
Release : 2016-10-18
Category : Science
ISBN : 9783319438023
This book discusses several recent theoretic advancements in interdisciplinary and transdisciplinary integration in the field of evolution. While exploring novel views, the text maintains a close link with one of the most broadly held views on evolution, namely that of “Darwinian evolution.” This work puts forth a new point of view which allows researchers to define in detail the concept of evolution. To create this conceptual definition, the text applies a stringent object-based focus. With this focus, the editor has been able to develop an object-based pattern of evolution at the smallest scale. Subsequently, this smallest scale pattern is used as an innovative basis for generalizations. These generalizations create links between biological Darwinism and generalized Darwinism. The object-based approach that was used to suggest innovations in the field of Darwinian evolution also allowed for contributions to other topics, such as major evolutionary transitions theory, the definition of life and the relationships between evolution, self-organization and thermodynamics. Together, the chapters of this book and the multidisciplinary reflections and comments of various specialists on these chapters offer an exciting palette of innovative ideas.
Author : Palle Jorgensen,Erin P J Pearse
Publisher : World Scientific
Page : 449 pages
File Size : 53,6 Mb
Release : 2023-03-21
Category : Mathematics
ISBN : 9789811265532
This volume considers resistance networks: large graphs which are connected, undirected, and weighted. Such networks provide a discrete model for physical processes in inhomogeneous media, including heat flow through perforated or porous media. These graphs also arise in data science, e.g., considering geometrizations of datasets, statistical inference, or the propagation of memes through social networks. Indeed, network analysis plays a crucial role in many other areas of data science and engineering. In these models, the weights on the edges may be understood as conductances, or as a measure of similarity. Resistance networks also arise in probability, as they correspond to a broad class of Markov chains.The present volume takes the nonstandard approach of analyzing resistance networks from the point of view of Hilbert space theory, where the inner product is defined in terms of Dirichlet energy. The resulting viewpoint emphasizes orthogonality over convexity and provides new insights into the connections between harmonic functions, operators, and boundary theory. Novel applications to mathematical physics are given, especially in regard to the question of self-adjointness of unbounded operators.New topics are covered in a host of areas accessible to multiple audiences, at both beginning and more advanced levels. This is accomplished by directly linking diverse applied questions to such key areas of mathematics as functional analysis, operator theory, harmonic analysis, optimization, approximation theory, and probability theory.
