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Random Operator Theory

Random Operator Theory
  • Author : Reza Saadati
  • Publisher :Unknown
  • Release Date :2016-08-24
  • Total pages :82
  • ISBN : 9780081009550
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Summary : Random Operator Theory provides a comprehensive discussion of the random norm of random bounded linear operators, also providing important random norms as random norms of differentiation operators and integral operators. After providing the basic definition of random norm of random bounded linear operators, the book then delves into the study of random operator theory, with final sections discussing the concept of random Banach algebras and its applications. Explores random differentiation and random integral equations Delves into the study of random operator theory Discusses the concept of random Banach algebras and its applications

Random Operators

Random Operators
  • Author : Michael Aizenman,Simone Warzel
  • Publisher :Unknown
  • Release Date :2015-12-11
  • Total pages :326
  • ISBN : 9781470419134
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Summary : This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization--presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and related results. The text incorporates notes from courses that were presented at the authors' respective institutions and attended by graduate students and postdoctoral researchers.

Spectral Theory of Random Schrödinger Operators

Spectral Theory of Random Schrödinger Operators
  • Author : R. Carmona,J. Lacroix
  • Publisher :Unknown
  • Release Date :2012-12-06
  • Total pages :589
  • ISBN : 9781461244882
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Summary : Since the seminal work of P. Anderson in 1958, localization in disordered systems has been the object of intense investigations. Mathematically speaking, the phenomenon can be described as follows: the self-adjoint operators which are used as Hamiltonians for these systems have a ten dency to have pure point spectrum, especially in low dimension or for large disorder. A lot of effort has been devoted to the mathematical study of the random self-adjoint operators relevant to the theory of localization for disordered systems. It is fair to say that progress has been made and that the un derstanding of the phenomenon has improved. This does not mean that the subject is closed. Indeed, the number of important problems actually solved is not larger than the number of those remaining. Let us mention some of the latter: • A proof of localization at all energies is still missing for two dimen sional systems, though it should be within reachable range. In the case of the two dimensional lattice, this problem has been approached by the investigation of a finite discrete band, but the limiting pro cedure necessary to reach the full two-dimensional lattice has never been controlled. • The smoothness properties of the density of states seem to escape all attempts in dimension larger than one. This problem is particularly serious in the continuous case where one does not even know if it is continuous.

Library of Congress Subject Headings

Library of Congress Subject Headings
  • Author : Library of Congress
  • Publisher :Unknown
  • Release Date :2005
  • Total pages :229
  • ISBN : STANFORD:36105118576763
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Summary :

Application of Linear Stochastic Operator Theory

Application of Linear Stochastic Operator Theory
  • Author : Leon H. Sibul
  • Publisher :Unknown
  • Release Date :1968
  • Total pages :340
  • ISBN : STANFORD:36105030431055
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Summary : In diverse areas of physics and engineering, problems arise which should properly be described by linear differential equations with stochastic coefficients. Methods are developed here for finding integral expressions for the second-order statistics (means, correlation functions and power spectrum) of the dependent variable of an nth order linear stochastic differential equation. These expressions constitute a generalization of the corresponding expressions for linear time-varying systems to linear randomly time-varying systems. The kernels of the integral expressions for the statistical measures of the solution can be interpreted as stochastic Green's functions.

Recent Trends in Operator Theory and Partial Differential Equations

Recent Trends in Operator Theory and Partial Differential Equations
  • Author : Vladimir Maz'ya,David Natroshvili,Eugene Shargorodsky,Wolfgang L. Wendland
  • Publisher :Unknown
  • Release Date :2017-02-23
  • Total pages :300
  • ISBN : 9783319470795
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Summary : This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research. The book is addressed to a wide audience of pure and applied mathematicians.

Introduction to Operator Space Theory

Introduction to Operator Space Theory
  • Author : Gilles Pisier
  • Publisher :Unknown
  • Release Date :2003-08-25
  • Total pages :478
  • ISBN : 0521811651
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Summary : Table of contents

Random linear operators

Random linear operators
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :1984
  • Total pages :229
  • ISBN : UCAL:B4979632
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Summary :

Spectral Theory and Mathematical Physics

Spectral Theory and Mathematical Physics
  • Author : Marius Mantoiu,Georgi Raikov,Rafael Tiedra de Aldecoa
  • Publisher :Unknown
  • Release Date :2016-06-30
  • Total pages :255
  • ISBN : 9783319299921
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Summary : The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schrödinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics. It will be of interest to researchers and graduate students in Mathematics and Mathematical Physics.

Random Linear Operators

Random Linear Operators
  • Author : A.V. Skorohod
  • Publisher :Unknown
  • Release Date :2001-11-30
  • Total pages :200
  • ISBN : 1402003269
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Summary : It isn't that they can't see Approach your problems from the solution. the right end and begin with It is that they can't see the the answers. Then one day, perhaps you will find the problem. final question. G. K. Chesterton. The Scandal 'The Hermit Clad in Crane of Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze l1urders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Spectral Theory and Differential Operators

Spectral Theory and Differential Operators
  • Author : E. Brian Davies,Edward Brian Davies
  • Publisher :Unknown
  • Release Date :1996-10-24
  • Total pages :182
  • ISBN : 0521587107
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Summary : This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on partial differential operators.

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

Convex Analysis and Monotone Operator Theory in Hilbert Spaces
  • Author : Heinz H. Bauschke,Patrick L. Combettes
  • Publisher :Unknown
  • Release Date :2017-02-28
  • Total pages :619
  • ISBN : 9783319483115
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Summary : 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.

Spectral Operator Theory and Related Topics

Spectral Operator Theory and Related Topics
  • Author : Vladimir Aleksandrovich Marchenko
  • Publisher :Unknown
  • Release Date :1994
  • Total pages :286
  • ISBN : CORNELL:31924068045834
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Summary : This collection contains papers by participants in the Seminar on Mathematical Physics in Kharkov, Ukraine. The papers mainly focus on nontraditional problems of spectral theory, such as new types of inverse problems for one-dimensional differential operators, new classes of solutions to nonlinear differential equations obtained using spectral methods, distribution of eigenvalues of large random matrices, and related problems of statistical physics of disordered systems. In addition, the papers explore the spectral aspects of homogenization and of properties of ergodic dynamical systems. All the papers contain original results published for the first time.

Random Walks on Reductive Groups

Random Walks on Reductive Groups
  • Author : Yves Benoist,Jean-François Quint
  • Publisher :Unknown
  • Release Date :2016-10-20
  • Total pages :323
  • ISBN : 9783319477213
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Summary : The classical theory of random walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.

Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :1976
  • Total pages :229
  • ISBN : UOM:49015003188381
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Summary :

Mathematics in Science and Engineering

Mathematics in Science and Engineering
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :1972
  • Total pages :229
  • ISBN : UIUC:30112007276162
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Summary :

The Theory of Quantum Information

The Theory of Quantum Information
  • Author : John Watrous
  • Publisher :Unknown
  • Release Date :2018-04-26
  • Total pages :598
  • ISBN : 9781107180567
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Summary : Formal development of the mathematical theory of quantum information with clear proofs and exercises. For graduate students and researchers.

Products of Random Matrices with Applications to Schrödinger Operators

Products of Random Matrices with Applications to Schrödinger Operators
  • Author : P. Bougerol,Lacroix
  • Publisher :Unknown
  • Release Date :2012-12-06
  • Total pages :284
  • ISBN : 9781468491722
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Summary : CHAPTER I THE DETERMINISTIC SCHRODINGER OPERATOR 187 1. The difference equation. Hyperbolic structures 187 2. Self adjointness of H. Spectral properties . 190 3. Slowly increasing generalized eigenfunctions 195 4. Approximations of the spectral measure 196 200 5. The pure point spectrum. A criterion 6. Singularity of the spectrum 202 CHAPTER II ERGODIC SCHRÖDINGER OPERATORS 205 1. Definition and examples 205 2. General spectral properties 206 3. The Lyapunov exponent in the general ergodie case 209 4. The Lyapunov exponent in the independent eas e 211 5. Absence of absolutely continuous spectrum 221 224 6. Distribution of states. Thouless formula 232 7. The pure point spectrum. Kotani's criterion 8. Asymptotic properties of the conductance in 234 the disordered wire CHAPTER III THE PURE POINT SPECTRUM 237 238 1. The pure point spectrum. First proof 240 2. The Laplace transform on SI(2,JR) 247 3. The pure point spectrum. Second proof 250 4. The density of states CHAPTER IV SCHRÖDINGER OPERATORS IN A STRIP 2';3 1. The deterministic Schrödinger operator in 253 a strip 259 2. Ergodie Schrödinger operators in a strip 3. Lyapunov exponents in the independent case. 262 The pure point spectrum (first proof) 267 4. The Laplace transform on Sp(~,JR) 272 5. The pure point spectrum, second proof vii APPENDIX 275 BIBLIOGRAPHY 277 viii PREFACE This book presents two elosely related series of leetures. Part A, due to P.

Mathematical Sciences Research Hot-line

Mathematical Sciences Research Hot-line
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :1997
  • Total pages :229
  • ISBN : UOM:39015046537398
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Summary :

Random Schrödinger Operators

Random Schrödinger Operators
  • Author : Margherita Disertori,Werner Kirsch,Abel Klein
  • Publisher :Unknown
  • Release Date :2008
  • Total pages :213
  • ISBN : UOM:39015072684635
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Summary : During the last thirty years, random Schrodinger operators, which originated in condensed matter physics, have been studied intensively and very productively. The theory is at the crossroads of a number of mathematical fields: the theory of operators, partial differential equations, the theory of probabilities, in particular the study of stochastic processes and that of random walks and Brownian motion in a random environment. This monograph aims to give the reader a panorama of the subject, from the now-classic foundations to very recent developments.

Operator Theory with a Random Potential, and Some Questions of Statistical Physics

Operator Theory with a Random Potential, and Some Questions of Statistical Physics
  • Author : Viktor Nikolaevich Popov
  • Publisher :Unknown
  • Release Date :1991
  • Total pages :259
  • ISBN : 0821831399
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Summary : This collection is devoted to problems of operator theory with a random potential and a number of problems of statistical physics. For the Schrodinger operator with a potential randomly depending on time, mean wave operators, and the mean scattering operator are computed, and it is shown that the averaged dynamics behaves like free dynamics in the limit of infinite time. Results of applying the method of functional integration to some problems of statistical physics are presented: the theory of systems with model Hamiltonians and their dynamics, ferromagnetic systems of spin 1/2, Coulomb and quantum crystals. This collection is intended for specialists in spectral theory and statistical physics.