Random Operator Theory Book

Random Operator Theory


  • Author : Reza Saadati
  • Publisher : Academic Press
  • Release Date : 2016-08-24
  • Genre: Mathematics
  • Pages : 82
  • ISBN 10 : 9780081009550

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Random Operator Theory Excerpt :

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 Integral Equations Book

Random Integral Equations


  • Author : Bharucha-Reid
  • Publisher : Academic Press
  • Release Date : 1973-03-02
  • Genre: Computers
  • Pages : 266
  • ISBN 10 : 9780080956053

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Random Integral Equations Excerpt :

Random Integral Equations

Random Operators Book

Random Operators


  • Author : Michael Aizenman
  • Publisher : American Mathematical Soc.
  • Release Date : 2015-12-11
  • Genre: Functional analysis -- Miscellaneous applications of functional analysis -- Applications in quantum physics
  • Pages : 326
  • ISBN 10 : 9781470419134

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Random Operators Excerpt :

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.

Random Operator Theory Book

Random Operator Theory


  • Author : Reza Saadati
  • Publisher : Academic Press
  • Release Date : 2016-08-17
  • Genre: Uncategoriezed
  • Pages : 82
  • ISBN 10 : 0128053461

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Random Operator Theory Excerpt :

"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 equationsDelves into the study of random operator theoryDiscusses the concept of random Banach algebras and its applications

Recent Trends in Operator Theory and Partial Differential Equations Book

Recent Trends in Operator Theory and Partial Differential Equations


  • Author : Vladimir Maz'ya
  • Publisher : Birkhäuser
  • Release Date : 2017-02-23
  • Genre: Mathematics
  • Pages : 300
  • ISBN 10 : 9783319470795

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Recent Trends in Operator Theory and Partial Differential Equations Excerpt :

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.

Random Linear Operators Book

Random Linear Operators


  • Author : A.V. Skorohod
  • Publisher : Springer Science & Business Media
  • Release Date : 2001-11-30
  • Genre: Mathematics
  • Pages : 220
  • ISBN 10 : 1402003269

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Random Linear Operators Excerpt :

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.

Eigenvalue Distribution of Large Random Matrices Book

Eigenvalue Distribution of Large Random Matrices


  • Author : Leonid Andreevich Pastur
  • Publisher : American Mathematical Soc.
  • Release Date : 2011
  • Genre: Mathematics
  • Pages : 632
  • ISBN 10 : 9780821852859

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Eigenvalue Distribution of Large Random Matrices Excerpt :

Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries). The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and self-contained treatment of the basic random matrix ensembles and asymptotic regimes. This book will be an important reference for researchers in a variety of areas of mathematics and mathematical physics. Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.

Nonlinear Operator Theory in Probablistic Metric Spaces Book

Nonlinear Operator Theory in Probablistic Metric Spaces


  • Author : Shih-sen Chang
  • Publisher : Nova Publishers
  • Release Date : 2001
  • Genre: Mathematics
  • Pages : 338
  • ISBN 10 : 1560729805

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Nonlinear Operator Theory in Probablistic Metric Spaces Excerpt :

The purpose of this book is to give a comprehensive introduction to the study of non-linear operator theory in probabilistic metric spaces. This book is introduced as a survey of the latest and new results on the following topics: Basic theory of probabilistic metric spaces; Fixed point theorems for single-valued and multi-valued mappings in probabilistic metric spaces; Ekeland's variational principle and Caristi's fixed point theorem in probabilistic metric spaces; Coincidence point theorems, minimisation and fixed degree theorems in probabilistic metric spaces; Probabilistic contractors, accretive mappings and topological degree in probabilistic normed spaces; Nonlinear semigroups and differential equations in probabilistic metric spaces; KKM theorems, minimax theorems and variational inequalities.

Spectral Theory of Random Schr  dinger Operators Book

Spectral Theory of Random Schr dinger Operators


  • Author : R. Carmona
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Mathematics
  • Pages : 589
  • ISBN 10 : 9781461244882

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Spectral Theory of Random Schr dinger Operators Excerpt :

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.

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

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


  • Author : Viktor Nikolaevich Popov
  • Publisher : American Mathematical Soc.
  • Release Date : 1991
  • Genre: Mathematics
  • Pages : 278
  • ISBN 10 : 0821831399

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

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.

Spectral Operator Theory and Related Topics Book

Spectral Operator Theory and Related Topics


  • Author : Vladimir Aleksandrovich Marchenko
  • Publisher : American Mathematical Soc.
  • Release Date : 1994
  • Genre: Differential operators
  • Pages : 300
  • ISBN 10 : 082184122X

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Spectral Operator Theory and Related Topics Excerpt :

"The collection contains the papers of mathematicians who are participants of the seminar on Mathematical Physics in Kharkov, Ukraine. The papers are mainly devoted to nontraditional problems of spectral theory, of disordered systems, to the spectral aspects of homogenization, and of properties of ergodic dynamical systems."--ABSTRACT.

The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities Book

The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities


  • Author : George Xian-Zhi Yuan
  • Publisher : American Mathematical Soc.
  • Release Date : 1998
  • Genre: Mathematics
  • Pages : 140
  • ISBN 10 : 9780821807477

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The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities Excerpt :

This book provides a unified treatment for the study of the existence of equilibria of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities, which strongly depend on his infinite dimensional version of the classical Knaster, Kuratowski and Mazurkiewicz Lemma (KKM Lemma) in 1961. Studied are applications of general system versions of minimax inequalities and generalized quasi-variational inequalities, and random abstract economies and its applications to the system of random quasi-variational inequalities are given. This work: presents new results and recent development of KKM theory; offers an overview of modern and up-to-date treatment of the KKM theory, including related articles covering theory and applications; uses an interdisciplinary approach with specific applications in mathematics and economics; and, includes a comprehensive bibliography.

Non Linear Mathematics Vol  II Book

Non Linear Mathematics Vol II


  • Author : Thomas L. Saaty
  • Publisher : RWS Publications
  • Release Date : 2014-12-22
  • Genre: Business & Economics
  • Pages : 480
  • ISBN 10 : 9781888603392

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Non Linear Mathematics Vol II Excerpt :

Nonlinear equations have existed for hundreds of years; their systematic study, however, is a relatively recent phenomenon. This volume, together with its companion', Nonlinear Matliematics Vol. I, provides exceptionally comprehensive coverage of this recently formed area of study. It encompasses both older and more recent developments in the field of equations, with particular emphasis on nonlinear equations because, as Professor Saaty maintains, "that is what is needed today." Together the two volumes cover all the major types of classical equations (except partial differential equations, which require a separate volume). This volume includes material on seven types: operator equations, functional equations, difference equations, delay-differential equations, integral equations, integro-differential equations and stochastic differential equations. Special emphasis is placed on linear and nonlinear equations in function spaces and On general methods of solving different types of such equations. Above all, this book is practical. It reviews the variety of existing types of equations and provides methods for their solution. It is meant to help the reader acquire new methods for formulating problems. Its clear organization and copious references make it suitable for graduate students as well as scientists, technologists and mathematicians.