Random Linear Operators

Author : A.V. Skorohod
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 42,9 Mb
Release : 2001-11-30
Category : Mathematics
ISBN : 1402003269

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Random Linear Operators by A.V. Skorohod Pdf

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.

Author : Reza Saadati
Publisher : Academic Press
Page : 82 pages
File Size : 44,7 Mb
Release : 2016-08-24
Category : Mathematics
ISBN : 9780081009550

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Random Operator Theory by Reza Saadati Pdf

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

Author : V.L. Girko
Publisher : Springer Science & Business Media
Page : 703 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400918580

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Theory of Random Determinants by V.L. Girko Pdf

'Et mm. ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point all':'' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf IIClI.t to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Author : Tailen Hsing,Randall Eubank
Publisher : John Wiley & Sons
Page : 368 pages
File Size : 53,8 Mb
Release : 2015-04-07
Category : Mathematics
ISBN : 9781118762578

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Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by Tailen Hsing,Randall Eubank Pdf

Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.

Author : Efstathia Bura,Bing Li
Publisher : Springer Nature
Page : 200 pages
File Size : 45,9 Mb
Release : 2021-04-27
Category : Mathematics
ISBN : 9783030690090

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Festschrift in Honor of R. Dennis Cook by Efstathia Bura,Bing Li Pdf

In honor of professor and renowned statistician R. Dennis Cook, this festschrift explores his influential contributions to an array of statistical disciplines ranging from experimental design and population genetics, to statistical diagnostics and all areas of regression-related inference and analysis. Since the early 1990s, Prof. Cook has led the development of dimension reduction methodology in three distinct but related regression contexts: envelopes, sufficient dimension reduction (SDR), and regression graphics. In particular, he has made fundamental and pioneering contributions to SDR, inventing or co-inventing many popular dimension reduction methods, such as sliced average variance estimation, the minimum discrepancy approach, model-free variable selection, and sufficient dimension reduction subspaces. A prolific researcher and mentor, Prof. Cook is known for his ability to identify research problems in statistics that are both challenging and important, as well as his deep appreciation for the applied side of statistics. This collection of Prof. Cook's collaborators, colleagues, friends, and former students reflects the broad array of his contributions to the research and instructional arenas of statistics.

Author : O. Bratteli,P.E.T. Jørgensen
Publisher : Springer Science & Business Media
Page : 200 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400964846

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Positive Semigroups of Operators, and Applications by O. Bratteli,P.E.T. Jørgensen Pdf

This means that semigroup theory may be applied directly to the study of the equation I'!.f = h on M. In [45] Yau proves that, for h ~ 0, there are no nonconstant, nonnegative solutions f in [j' for 1

Author : George A. Anastassiou
Publisher : Springer
Page : 444 pages
File Size : 49,9 Mb
Release : 2010-03-17
Category : Technology & Engineering
ISBN : 9783642112201

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Fuzzy Mathematics: Approximation Theory by George A. Anastassiou Pdf

This monograph is the r st in Fuzzy Approximation Theory. It contains mostly the author s research work on fuzziness of the last ten years and relies a lot on [10]-[32] and it is a natural outgrowth of them. It belongs to the broader area of Fuzzy Mathematics. Chapters are self-contained and several advanced courses can be taught out of this book. We provide lots of applications but always within the framework of Fuzzy Mathematics. In each chapter is given background and motivations. A c- plete list of references is provided at the end. The topics covered are very diverse. In Chapter 1 we give an extensive basic background on Fuzziness and Fuzzy Real Analysis, as well a complete description of the book. In the following Chapters 2,3 we cover in deep Fuzzy Di?erentiation and Integ- tion Theory, e.g. we present Fuzzy Taylor Formulae. It follows Chapter 4 on Fuzzy Ostrowski Inequalities. Then in Chapters 5, 6 we present results on classical algebraic and trigonometric polynomial Fuzzy Approximation.

Author : A. T. Bharucha-Reid
Publisher : Elsevier
Page : 271 pages
File Size : 41,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483275468

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Probabilistic Analysis and Related Topics by A. T. Bharucha-Reid Pdf

Probabilistic Analysis and Related Topics, Volume 3 focuses on the continuity, integrability, and differentiability of random functions, including operator theory, measure theory, and functional and numerical analysis. The selection first offers information on the qualitative theory of stochastic systems and Langevin equations with multiplicative noise. Discussions focus on phase-space evolution via direct integration, phase-space evolution, linear and nonlinear systems, linearization, and generalizations. The text then ponders on the stability theory of stochastic difference systems and Markov properties for random fields. Topics include Markov property of solutions of stochastic partial differential equations; Markov property for generalized Gaussian random fields; Markov properties for generalized random fields; stochastic stability of nonlinear systems; and linear stochastic systems. The publication examines the method of random contractors and its applications to random nonlinear equations, including integral contractors and applications to random equations; random contractors with random nonlinear majorant functions; and random contractors and application to random nonlinear operator equations. The selection is a valuable reference for mathematicians and researchers interested in the general theory of random functions.

Author : David Applebaum
Publisher : Cambridge University Press
Page : 235 pages
File Size : 44,5 Mb
Release : 2019-08-15
Category : Mathematics
ISBN : 9781108623520

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Semigroups of Linear Operators by David Applebaum Pdf

The theory of semigroups of operators is one of the most important themes in modern analysis. Not only does it have great intellectual beauty, but also wide-ranging applications. In this book the author first presents the essential elements of the theory, introducing the notions of semigroup, generator and resolvent, and establishes the key theorems of Hille–Yosida and Lumer–Phillips that give conditions for a linear operator to generate a semigroup. He then presents a mixture of applications and further developments of the theory. This includes a description of how semigroups are used to solve parabolic partial differential equations, applications to Levy and Feller–Markov processes, Koopmanism in relation to dynamical systems, quantum dynamical semigroups, and applications to generalisations of the Riemann–Liouville fractional integral. Along the way the reader encounters several important ideas in modern analysis including Sobolev spaces, pseudo-differential operators and the Nash inequality.

Author : M. Zuhair Nashed
Publisher : Elsevier
Page : 1069 pages
File Size : 42,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483270296

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Generalized Inverses and Applications by M. Zuhair Nashed Pdf

Generalized Inverses and Applications, contains the proceedings of an Advanced Seminar on Generalized Inverses and Applications held at the University of Wisconsin-Madison on October 8-10, 1973 under the auspices of the university's Mathematics Research Center. The seminar provided a forum for discussing the basic theory of generalized inverses and their applications to analysis and operator equations. Numerical analysis and approximation methods are considered, along with applications to statistics and econometrics, optimization, system theory, and operations research. Comprised of 14 chapters, this book begins by describing a unified approach to generalized inverses of linear operators, with particular reference to algebraic, topological, extremal, and proximinal properties. The reader is then introduced to the algebraic aspects of the generalized inverse of a rectangular matrix; the Fredholm pseudoinverse; and perturbations and approximations for generalized inverses and linear operator equations. Subsequent chapters deal with various applications of generalized inverses, including programming, games, and networks, as well as estimation and aggregation in econometrics. This monograph will be of interest to mathematicians and students of mathematics.

Author : Albert T. Bharucha-Reid
Publisher : North-Holland
Page : 264 pages
File Size : 46,7 Mb
Release : 1979
Category : Approximation theory
ISBN : UCAL:B4405415

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Approximate Solution of Random Equations by Albert T. Bharucha-Reid Pdf

Author : Tailen Hsing,Randall Eubank
Publisher : John Wiley & Sons
Page : 362 pages
File Size : 40,8 Mb
Release : 2015-05-06
Category : Mathematics
ISBN : 9780470016916

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Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by Tailen Hsing,Randall Eubank Pdf

Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.

Author : E. Brian Davies
Publisher : Cambridge University Press
Page : 436 pages
File Size : 46,7 Mb
Release : 2007-04-26
Category : Mathematics
ISBN : 9781139464338

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Linear Operators and their Spectra by E. Brian Davies Pdf

This wide ranging but self-contained account of the spectral theory of non-self-adjoint linear operators is ideal for postgraduate students and researchers, and contains many illustrative examples and exercises. Fredholm theory, Hilbert-Schmidt and trace class operators are discussed, as are one-parameter semigroups and perturbations of their generators. Two chapters are devoted to using these tools to analyze Markov semigroups. The text also provides a thorough account of the new theory of pseudospectra, and presents the recent analysis by the author and Barry Simon of the form of the pseudospectra at the boundary of the numerical range. This was a key ingredient in the determination of properties of the zeros of certain orthogonal polynomials on the unit circle. Finally, two methods, both very recent, for obtaining bounds on the eigenvalues of non-self-adjoint Schrodinger operators are described. The text concludes with a description of the surprising spectral properties of the non-self-adjoint harmonic oscillator.

Author : Xiaojun Yuan,Zhipeng Xue
Publisher : Springer Nature
Page : 105 pages
File Size : 43,9 Mb
Release : 2020-10-13
Category : Technology & Engineering
ISBN : 9783030547622

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Turbo Message Passing Algorithms for Structured Signal Recovery by Xiaojun Yuan,Zhipeng Xue Pdf

This book takes a comprehensive study on turbo message passing algorithms for structured signal recovery, where the considered structured signals include 1) a sparse vector/matrix (which corresponds to the compressed sensing (CS) problem), 2) a low-rank matrix (which corresponds to the affine rank minimization (ARM) problem), 3) a mixture of a sparse matrix and a low-rank matrix (which corresponds to the robust principal component analysis (RPCA) problem). The book is divided into three parts. First, the authors introduce a turbo message passing algorithm termed denoising-based Turbo-CS (D-Turbo-CS). Second, the authors introduce a turbo message passing (TMP) algorithm for solving the ARM problem. Third, the authors introduce a TMP algorithm for solving the RPCA problem which aims to recover a low-rank matrix and a sparse matrix from their compressed mixture. With this book, we wish to spur new researches on applying message passing to various inference problems. Provides an in depth look into turbo message passing algorithms for structured signal recovery Includes efficient iterative algorithmic solutions for inference, optimization, and satisfaction problems through message passing Shows applications in areas such as wireless communications and computer vision

Author : Evarist Giné
Publisher : IMS
Page : 288 pages
File Size : 42,8 Mb
Release : 2006
Category : Mathematics
ISBN : 0940600676

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High Dimensional Probability by Evarist Giné Pdf