Random Operator Theory

Random Operator Theory
Author: Reza Saadati
Publsiher: Academic Press
Total Pages: 82
Release: 2016-08-24
Genre: Mathematics
ISBN: 9780081009550

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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

Random Integral Equations
Author: Bharucha-Reid
Publsiher: Academic Press
Total Pages: 266
Release: 1973-03-02
Genre: Computers
ISBN: 9780080956053

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Random Integral Equations

Random Operators

Random Operators
Author: Michael Aizenman,Simone Warzel
Publsiher: American Mathematical Soc.
Total Pages: 326
Release: 2015-12-11
Genre: Functional analysis -- Miscellaneous applications of functional analysis -- Applications in quantum physics
ISBN: 9781470419134

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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

Random Operator Theory
Author: Reza Saadati
Publsiher: Academic Press
Total Pages: 82
Release: 2016-08-17
Genre: Electronic Book
ISBN: 0128053461

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"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

Recent Trends in Operator Theory and Partial Differential Equations
Author: Vladimir Maz'ya,David Natroshvili,Eugene Shargorodsky,Wolfgang L. Wendland
Publsiher: Birkhäuser
Total Pages: 300
Release: 2017-02-23
Genre: Mathematics
ISBN: 9783319470795

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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

Random Linear Operators
Author: A.V. Skorohod
Publsiher: Springer Science & Business Media
Total Pages: 220
Release: 2001-11-30
Genre: Mathematics
ISBN: 1402003269

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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

Eigenvalue Distribution of Large Random Matrices
Author: Leonid Andreevich Pastur,Mariya Shcherbina
Publsiher: American Mathematical Soc.
Total Pages: 632
Release: 2011
Genre: Mathematics
ISBN: 9780821852859

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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

Nonlinear Operator Theory in Probablistic Metric Spaces
Author: Shih-sen Chang,Yeol Je Cho,Sin-min Kang
Publsiher: Nova Publishers
Total Pages: 338
Release: 2001
Genre: Mathematics
ISBN: 1560729805

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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.