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New Difference Schemes for Partial Differential Equations

Posted By: AvaxGenius
New Difference Schemes for Partial Differential Equations

New Difference Schemes for Partial Differential Equations by Allaberen Ashyralyev , Pavel E. Sobolevskii
English | PDF | 2004 | 453 Pages | ISBN : 3764370548 | 48.7 MB

The present monograph is devoted to the construction and investigation of the new high order of accuracy difference schemes of approximating the solutions of regular and singular perturbation boundary value problems for partial differential equations. The construction is based on the exact difference scheme and Taylor's decomposition on the two or three points. This approach permitted essentially to extend to a class of problems where the theory of difference methods is applicable. Namely, now it is possible to investigate the differential equations with variable coefficients and regular and singular perturbation boundary value problems. The investigation is based on new coercivity inequalities.

Nigel J. Kalton Selecta: Volume 2 (Repost)

Posted By: AvaxGenius
Nigel J. Kalton Selecta: Volume 2 (Repost)

Nigel J. Kalton Selecta: Volume 2 by Fritz Gesztesy, Gilles Godefroy, Loukas Grafakos, Igor Verbitsky
English | PDF (True | 2016 | 778 Pages | ISBN : 3319187988 | 262.5 MB

This is the second part of a two volume anthology comprising a selection of 49 articles that illustrate the depth, breadth and scope of Nigel Kalton’s research. Each article is accompanied by comments from an expert on the respective topic, which serves to situate the article in its proper context, to successfully link past, present and hopefully future developments of the theory and to help readers grasp the extent of Kalton’s accomplishments. Kalton’s work represents a bridge to the mathematics of tomorrow, and this book will help readers to cross it.

Renormalized Quantum Field Theory

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Renormalized Quantum Field Theory

Renormalized Quantum Field Theory by O. I. Zavialov
English | PDF | 1990 | 537 Pages | ISBN : 9027727589 | 31.6 MB

This book is concerned with the mathematical aspects of renormalization theory. Part of it was written in 1978 and published under the title 'Renormalized Feynman Diagrams' -in Russian in 1979. The present English edition is, in a sense, a quite new book. The old text has been thoroughly revised and new chapters have been added.

Dilations, Completely Positive Maps and Geometry

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Dilations, Completely Positive Maps and Geometry

Dilations, Completely Positive Maps and Geometry by B.V. Rajarama Bhat , Tirthankar Bhattacharyya
English | PDF EPUB (True) | 223 | 236 Pages | ISBN : 9819983517 | 27.8 MB

This book introduces the dilation theory of operators on Hilbert spaces and its relationship to complex geometry. Classical as well as very modern topics are covered in the book. On the one hand, it introduces the reader to the characteristic function, a classical object used by Sz.-Nagy and Foias and still a topic of current research. On the other hand, it describes the dilation theory of the symmetrized bidisc which has been developed mostly in the present century and is a very active topic of research. It also describes an abstract theory of dilation in the setting of set theory. This was developed very recently.

Real and Stochastic Analysis: New Perspectives

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Real and Stochastic Analysis: New Perspectives

Real and Stochastic Analysis: New Perspectives by M. M. Rao
English | PDF | 2004 | 411 Pages | ISBN : 081764332X | 45.9 MB

As in the case of the two previous volumes published in 1986 and 1997, the purpose of this monograph is to focus the interplay between real (functional) analysis and stochastic analysis show their mutual benefits and advance the subjects. The presentation of each article, given as a chapter, is in a research-expository style covering the respective topics in depth. In fact, most of the details are included so that each work is essentially self contained and thus will be of use both for advanced graduate students and other researchers interested in the areas considered. Moreover, numerous new problems for future research are suggested in each chapter. The presented articles contain a substantial number of new results as well as unified and simplified accounts of previously known ones. A large part of the material cov­ ered is on stochastic differential equations on various structures, together with some applications. Although Brownian motion plays a key role, (semi-) martingale theory is important for a considerable extent. Moreover, noncommutative analysis and probabil­ ity have a prominent role in some chapters, with new ideas and results. A more detailed outline of each of the articles appears in the introduction and outline to assist readers in selecting and starting their work. All chapters have been reviewed.

Positivity (Repost)

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Positivity (Repost)

Positivity by Karim Boulabiar, Gerard Buskes, Abdelmajid Triki
English | PDF (True) | 2007 | 282 Pages | ISBN : 3764384778 | 2.5 MB

This book presents nine survey articles addressing topics surrounding positivity, with an emphasis on functional analysis. The book assembles a wide spectrum of research into positivity, providing up-to-date information on topics of current interest. The discussion provides insight into classical areas like spaces of continuous functions, f-algebras, and integral operators. The coverage extends is broad, including vector measures, operator spaces, ordered tensor products, and non-commutative Banach function spaces.

C*-algebras and Elliptic Theory II (Repost)

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C*-algebras and Elliptic Theory II (Repost)

C*-algebras and Elliptic Theory II by Dan Burghelea, Richard Melrose, Alexander S. Mishchenko, Evgenij V. Troitsky
English | PDF (True) | 2008 | 312 Pages | ISBN : 3764386037 | 2.7 MB

This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.

Nonlinear Inclusions and Hemivariational Inequalities: Models and Analysis of Contact Problems (Repost)

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Nonlinear Inclusions and Hemivariational Inequalities: Models and Analysis of Contact Problems (Repost)

Nonlinear Inclusions and Hemivariational Inequalities: Models and Analysis of Contact Problems by Stanisław Migórski , Anna Ochal , Mircea Sofonea
English | PDF (True) | 2013 | 293 Pages | ISBN : 1461442311 | 3 MB

This book introduces the reader the theory of nonlinear inclusions and hemivariational inequalities with emphasis on the study of contact mechanics. The work covers both abstract results in the area of nonlinear inclusions, hemivariational inequalities as well as the study of specific contact problems, including their modelling and their variational analysis. Provided results are based on original research on the existence, uniqueness, regularity and behavior of the solution for various classes of nonlinear stationary and evolutionary inclusions. In carrying out the variational analysis of various contact models, one systematically uses results of hemivariational inequalities and, in this way, illustrates the applications of nonlinear analysis in contact mechanics. New mathematical methods are introduced and applied in the study of nonlinear problems, which describe the contact between a deformable body and a foundation. Contact problems arise in industry, engineering and geophysics. Their variational analysis presented in this book lies the background for their numerical analysis. This volume will interest mathematicians, applied mathematicians, engineers, and scientists as well as advanced graduate students.

Approximate Solution of Operator Equations

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Approximate Solution of Operator Equations

Approximate Solution of Operator Equations by M. A. Krasnosel’skii , G. M. Vainikko , P. P. Zabreiko , Ya. B. Rutitskii , V. Ya. Stetsenko
English | PDF | 1972 | 495 Pages | ISBN : 940102717X | 32 MB

One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho­ nov's methods for approximate solution of ill-posed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni­ versity on the application of functional analysis to numerical mathe­ matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters.

Nigel J. Kalton Selecta: Volume 2

Posted By: AvaxGenius
Nigel J. Kalton Selecta: Volume 2

Nigel J. Kalton Selecta: Volume 2 by Fritz Gesztesy, Gilles Godefroy, Loukas Grafakos, Igor Verbitsky
English | PDF (True | 2016 | 778 Pages | ISBN : 3319187988 | 262.5 MB

This is the second part of a two volume anthology comprising a selection of 49 articles that illustrate the depth, breadth and scope of Nigel Kalton’s research. Each article is accompanied by comments from an expert on the respective topic, which serves to situate the article in its proper context, to successfully link past, present and hopefully future developments of the theory and to help readers grasp the extent of Kalton’s accomplishments. Kalton’s work represents a bridge to the mathematics of tomorrow, and this book will help readers to cross it.

Exploring Mathematical Analysis, Approximation Theory, and Optimization: 270 Years Since A.-M. Legendre’s Birth

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Exploring Mathematical Analysis, Approximation Theory, and Optimization: 270 Years Since A.-M. Legendre’s Birth

Exploring Mathematical Analysis, Approximation Theory, and Optimization: 270 Years Since A.-M. Legendre’s Birth by Nicholas J. Daras, Michael Th. Rassias, Nikolaos B. Zographopoulos
English | PDF EPUB (True) | 2023 | 474 Pages | ISBN : 3031464869 | 53.9 MB

This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education.

Semigroups of Linear and Nonlinear Operations and Applications

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Semigroups of Linear and Nonlinear Operations and Applications

Semigroups of Linear and Nonlinear Operations and Applications: Proceedings of the Curaçao Conference, August 1992 by Gisèle Ruiz Goldstein, Jerome A. Goldstein
English | PDF | 1993 | 280 Pages | ISBN : 0792325605 | 17.3 MB

This is the first publication which follows an agreement by Kluwer Publishers with the Caribbean Mathematics Foundation (CMF), to publish the proceedings of its mathematical activities. To which one should add a disclaimer of sorts, namely that this volume is not the first in a series, because it is not first, and be­ cause neither party to the agreement construes these publications as elements of a series. Like the work of CMF, the arrangement between it and Kluwer Publishers, evolved gradually, empirically. CMF was created in 1988, and inaugurated with a conference on Ordered Algebraic Structures. Every year since there have been gatherings on a variety of mathematical topics: Locales and Topological Groups in 1989; Positive Operators in 1990; Finite Geometry and Abelian Groups in 1991; Semigroups of Operators last year. It should be stressed, however that in preparing for the first conference, there was no plan which might have augured what came after. One could say that one thing led to another, and one would be right enough.

Function Spaces, Theory and Applications

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Function Spaces, Theory and Applications

Function Spaces, Theory and Applications by Ilia Binder, Damir Kinzebulatov, Javad Mashreghi
English | PDF EPUB (True) | 2023 | 487 Pages | ISBN : 3031392698 | 54.2 MB

The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They also have several essential applications in other fields of mathematics and engineering, e.g., robust control engineering, signal and image processing, and theory of communication. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins, e.g. the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b), have also been the center of attention in the past two decades. Studying the Hilbert spaces of analytic functions and the operators acting on them, as well as their applications in other parts of mathematics or engineering were the main subjects of this program. During the program, the world leading experts on function spaces gathered and discussed the new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains.

Analysis in Banach Spaces: Volume III: Harmonic Analysis and Spectral Theory

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Analysis in Banach Spaces: Volume III: Harmonic Analysis and Spectral Theory

Analysis in Banach Spaces: Volume III: Harmonic Analysis and Spectral Theory by Tuomas Hytönen , Jan van Neerven , Mark Veraar , Lutz Weis
English | PDF (True) | 2023 | 839 Pages | ISBN : 3031465970 | 15.2 MB

This third volume of Analysis in Banach Spaces offers a systematic treatment of Banach space-valued singular integrals, Fourier transforms, and function spaces. It further develops and ramifies the theory of functional calculus from Volume II and describes applications of these new notions and tools to the problem of maximal regularity of evolution equations. The exposition provides a unified treatment of a large body of results, much of which has previously only been available in the form of research papers. Some of the more classical topics are presented in a novel way using modern techniques amenable to a vector-valued treatment. Thanks to its accessible style with complete and detailed proofs, this book will be an invaluable reference for researchers interested in functional analysis, harmonic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.

Variational Methods in Theoretical Mechanics

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Variational Methods in Theoretical Mechanics

Variational Methods in Theoretical Mechanics by J. T. Oden , J. N. Reddy
English | PDF | 1976 | 313 Pages | ISBN : N/A | 21.2 MB

This is a textbook written for use in a graduate-level course for students of mechanics and engineering science. It is designed to cover the essential features of modern variational methods and to demonstrate how a number of basic mathematical concepts can be used to produce a unified theory of variational mechanics. As prerequisite to using this text, we assume that the student is equipped with an introductory course in functional analysis at a level roughly equal to that covered, for example, in Kolmogorov and Fomin (Functional Analysis, Vol. I, Graylock, Rochester, 1957) and possibly a graduate-level course in continuum mechanics. Numerous references to supplementary material are listed throughout the book. We are indebted to Professor Jim Douglas of the University of Chicago, who read an earlier version of the manuscript and whose detailed suggestions were extremely helpful in preparing the final draft. He also gratefully acknowledge that much of our own research work on variational theory was supported by the U.S. Air Force Office of Scientific Research. He are indebted to Mr. Ming-Goei Sheu for help in proofreading. Finally, we wish to express thanks to Mrs. Marilyn Gude for her excellent and pains­ taking job of typing the manuscript. J. T. ODEN J. N. REDDY Table of Contents PREFACE 1. INTRODUCTION 1.1 The Role of Variational Theory in Mechanics. 1 1.2 Some Historical Comments ……… . 2 1.3 Plan of Study …………… . 5 7 2. MATHEMATICAL FOUNDATIONS OF CLASSICAL VARIATIONAL THEORY 7 2.1 Introduction .