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Author : Jerry Peel
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.:/5 (126 download)
Download or read book The Lp Spaces of Equivalence Classes of Lebesgue Integrable Functions written by Jerry Peel and published by . This book was released on 1972 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert G. Bartle
Publisher : John Wiley & Sons
ISBN 13 : 1118626125
Total Pages : 121 pages
Book Rating : 4.1/5 (186 download)
Download or read book The Elements of Integration and Lebesgue Measure written by Robert G. Bartle and published by John Wiley & Sons. This book was released on 2014-08-21 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consists of two separate but closely related parts. Originally published in 1966, the first section deals with elements of integration and has been updated and corrected. The latter half details the main concepts of Lebesgue measure and uses the abstract measure space approach of the Lebesgue integral because it strikes directly at the most important results—the convergence theorems.
Author : J. Bourgain
Publisher : Springer
ISBN 13 : 3540386114
Total Pages : 147 pages
Book Rating : 4.5/5 (43 download)
Download or read book New Classes of Lp-Spaces written by J. Bourgain and published by Springer. This book was released on 2006-11-14 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this text is to present new examples of LP-spaces for 1 ≤ P ≤ ∞. This work has three reasons of interest. First, of course, it provides new LPspaces. Secondly, because certain constructions are based on new ideas and techniques with possibly other applications. Finally, especially in chapters four and five, crucial use is made of certain probabilistic results which have an independent importance.
Author : Open University. M431 Course Team
Publisher :
ISBN 13 : 9780749220686
Total Pages : 27 pages
Book Rating : 4.2/5 (26 download)
Download or read book The Lebesgue Integral written by Open University. M431 Course Team and published by . This book was released on 1992 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dragisa Mitrovic
Publisher : CRC Press
ISBN 13 : 9780582246942
Total Pages : 416 pages
Book Rating : 4.2/5 (469 download)
Download or read book Fundamentals of Applied Functional Analysis written by Dragisa Mitrovic and published by CRC Press. This book was released on 1997-11-12 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to modern concepts of linear and nonlinear functional analysis. Its purpose is also to provide an insight into the variety of deeply interlaced mathematical tools applied in the study of nonlinear problems.
Author : Eric W. Weisstein
Publisher : CRC Press
ISBN 13 : 1420035223
Total Pages : 3253 pages
Book Rating : 4.4/5 (2 download)
Download or read book CRC Concise Encyclopedia of Mathematics written by Eric W. Weisstein and published by CRC Press. This book was released on 2002-12-12 with total page 3253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d
Author : Jürgen Jost
Publisher : Springer Science & Business Media
ISBN 13 : 3662036355
Total Pages : 350 pages
Book Rating : 4.6/5 (62 download)
Download or read book Postmodern Analysis written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the title of this book intended to signify, what connotations is the adjective "Postmodern" meant to carry? A potential reader will surely pose this question. To answer it, I should describe what distinguishes the approach to analysis presented here from what has been called "Modern Analysis" by its protagonists. "Modern Analysis" as represented in the works of the Bour baki group or in the textbooks by Jean Dieudonne is characterized by its systematic and axiomatic treatment and by its drive towards a high level of abstraction. Given the tendency of many prior treatises on analysis to degen erate into a collection of rather unconnected tricks to solve special problems, this definitively represented a healthy achievement. In any case, for the de velopment of a consistent and powerful mathematical theory, it seems to be necessary to concentrate solelyon the internal problems and structures and to neglect the relations to other fields of scientific, even of mathematical study for a certain while. Almost complete isolation may be required to reach the level of intellectual elegance and perfection that only a good mathematical theory can acquire. However, once this level has been reached, it might be useful to open one's eyes again to the inspiration coming from concrete ex ternal problems.
Author : Petru A. Cioica
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832539204
Total Pages : 166 pages
Book Rating : 4.8/5 (325 download)
Download or read book Besov Regularity of Stochastic Partial Differential Equations on Bounded Lipschitz Domains written by Petru A. Cioica and published by Logos Verlag Berlin GmbH. This book was released on 2015-03-01 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic partial differential equations (SPDEs, for short) are the mathematical models of choice for space time evolutions corrupted by noise. Although in many settings it is known that the resulting SPDEs have a unique solution, in general, this solution is not given explicitly. Thus, in order to make those mathematical models ready to use for real life applications, appropriate numerical algorithms are needed. To increase efficiency, it would be tempting to design suitable adaptive schemes based, e.g., on wavelets. However, it is not a priori clear whether such adaptive strategies can outperform well-established uniform alternatives. Their theoretical justification requires a rigorous regularity analysis in so-called non-linear approximation scales of Besov spaces. In this thesis the regularity of (semi-)linear second order SPDEs of Itô type on general bounded Lipschitz domains is analysed. The non-linear approximation scales of Besov spaces are used to measure the regularity with respect to the space variable, the time regularity being measured first in terms of integrability and afterwards in terms of Hölder norms. In particular, it is shown that in specific situations the spatial Besov regularity of the solution in the non-linear approximation scales is generically higher than its corresponding classical Sobolev regularity. This indicates that it is worth developing spatially adaptive wavelet methods for solving SPDEs instead of using uniform alternatives.
Author : Nicolae Dinculeanu
Publisher : John Wiley & Sons
ISBN 13 : 1118031261
Total Pages : 446 pages
Book Rating : 4.1/5 (18 download)
Download or read book Vector Integration and Stochastic Integration in Banach Spaces written by Nicolae Dinculeanu and published by John Wiley & Sons. This book was released on 2011-09-28 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: A breakthrough approach to the theory and applications of stochastic integration The theory of stochastic integration has become an intensely studied topic in recent years, owing to its extraordinarily successful application to financial mathematics, stochastic differential equations, and more. This book features a new measure theoretic approach to stochastic integration, opening up the field for researchers in measure and integration theory, functional analysis, probability theory, and stochastic processes. World-famous expert on vector and stochastic integration in Banach spaces Nicolae Dinculeanu compiles and consolidates information from disparate journal articles-including his own results-presenting a comprehensive, up-to-date treatment of the theory in two major parts. He first develops a general integration theory, discussing vector integration with respect to measures with finite semivariation, then applies the theory to stochastic integration in Banach spaces. Vector Integration and Stochastic Integration in Banach Spaces goes far beyond the typical treatment of the scalar case given in other books on the subject. Along with such applications of the vector integration as the Reisz representation theorem and the Stieltjes integral for functions of one or two variables with finite semivariation, it explores the emergence of new classes of summable processes that make applications possible, including square integrable martingales in Hilbert spaces and processes with integrable variation or integrable semivariation in Banach spaces. Numerous references to existing results supplement this exciting, breakthrough work.
Author : L. P. Lebedev
Publisher : World Scientific
ISBN 13 : 981439047X
Total Pages : 500 pages
Book Rating : 4.8/5 (143 download)
Download or read book Advanced Engineering Analysis written by L. P. Lebedev and published by World Scientific. This book was released on 2012 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Engineering Analysis: The Calculus of Variations and Functional Analysis with Applications in Mechanics Advanced Engineering Analysis is a textbook on modern engineering analysis, covering the calculus of variations, functional analysis, and control theory, as well as applications of these disciplines to mechanics. The book offers a brief and concise, yet complete explanation of essential theory and applications. It contains exercises with hints and solutions, ideal for self-study. Book jacket.
Author : Ulrich Oberst
Publisher : Springer Nature
ISBN 13 : 3030439364
Total Pages : 757 pages
Book Rating : 4.0/5 (34 download)
Download or read book Linear Time-Invariant Systems, Behaviors and Modules written by Ulrich Oberst and published by Springer Nature. This book was released on 2020-06-27 with total page 757 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprehensively examines various significant aspects of linear time-invariant systems theory, both for continuous-time and discrete-time. Using a number of new mathematical methods it provides complete and exact proofs of all the systems theoretic and electrical engineering results, as well as important results and algorithms demonstrated with nontrivial computer examples. The book is intended for readers who have completed the first two years of a university mathematics course. All further mathematical results required are proven in the book.
Author : M.M. Rao
Publisher : CRC Press
ISBN 13 : 1482258102
Total Pages : 790 pages
Book Rating : 4.4/5 (822 download)
Download or read book Measure Theory and Integration written by M.M. Rao and published by CRC Press. This book was released on 2018-10-03 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types-providing a complete and detailed review of every aspect of measure and integration theory using valuable examples, exercises, and applications. With more than 170 references for further investigation of the subject, this Second Edition provides more than 60 pages of new information, as well as a new chapter on nonabsolute integrals contains extended discussions on the four basic results of Banach spaces presents an in-depth analysis of the classical integrations with many applications, including integration of nonmeasurable functions, Lebesgue spaces, and their properties details the basic properties and extensions of the Lebesgue-Carathéodory measure theory, as well as the structure and convergence of real measurable functions covers the Stone isomorphism theorem, the lifting theorem, the Daniell method of integration, and capacity theory Measure Theory and Integration, Second Edition is a valuable reference for all pure and applied mathematicians, statisticians, and mathematical analysts, and an outstanding text for all graduate students in these disciplines.
Author : Nikolaos S. Papageorgiou
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111286959
Total Pages : 734 pages
Book Rating : 4.1/5 (112 download)
Download or read book Applied Nonlinear Functional Analysis written by Nikolaos S. Papageorgiou and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-07-01 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition covers the introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics. The new edition includes some new topics on Banach spaces of functions and measures and nonlinear analysis.
Author : Hemant Kumar Pathak
Publisher : Springer
ISBN 13 : 9811088667
Total Pages : 830 pages
Book Rating : 4.8/5 (11 download)
Download or read book An Introduction to Nonlinear Analysis and Fixed Point Theory written by Hemant Kumar Pathak and published by Springer. This book was released on 2018-05-19 with total page 830 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book systematically introduces the theory of nonlinear analysis, providing an overview of topics such as geometry of Banach spaces, differential calculus in Banach spaces, monotone operators, and fixed point theorems. It also discusses degree theory, nonlinear matrix equations, control theory, differential and integral equations, and inclusions. The book presents surjectivity theorems, variational inequalities, stochastic game theory and mathematical biology, along with a large number of applications of these theories in various other disciplines. Nonlinear analysis is characterised by its applications in numerous interdisciplinary fields, ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to stochastic game theory. Organised into ten chapters, the book shows the elegance of the subject and its deep-rooted concepts and techniques, which provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in diverse applied fields. It is intended for graduate and undergraduate students of mathematics and engineering who are familiar with discrete mathematical structures, differential and integral equations, operator theory, measure theory, Banach and Hilbert spaces, locally convex topological vector spaces, and linear functional analysis.
Author : Ammar Khanfer
Publisher : Springer Nature
ISBN 13 : 9819930294
Total Pages : 450 pages
Book Rating : 4.8/5 (199 download)
Download or read book Fundamentals of Functional Analysis written by Ammar Khanfer and published by Springer Nature. This book was released on 2023-12-24 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a comprehensive exploration of functional analysis, covering a wide range of topics. With over 150 solved examples and more than 320 problems, the book is designed to be both motivational and user-friendly for students for senior undergraduate and graduate courses in mathematics, providing clear and thorough explanations of all concepts. The second volume in a three-part series, this book delves into normed spaces, linear functionals, locally convex spaces, Banach spaces, Hilbert spaces, topology of Banach spaces, operators on Banach spaces and geometry of Banach spaces. The text is written in a clear and engaging style, making it ideal for independent study. It offers a valuable source for students seeking a deeper understanding of functional analysis, and provides a solid understanding of the topic.
Author : Leonid P. Lebedev
Publisher : Springer Science & Business Media
ISBN 13 : 0387227253
Total Pages : 245 pages
Book Rating : 4.3/5 (872 download)
Download or read book Functional Analysis in Mechanics written by Leonid P. Lebedev and published by Springer Science & Business Media. This book was released on 2006-04-29 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers functional analysis and its applications to continuum mechanics.; The mathematical material is treated in a non-abstract manner and is fully illuminated by the underlying mechanical ideas.; The presentation is concise but complete, and is intended for specialists in continuum mechanics who wish to understand the mathematical underpinnings of the discipline.; Graduate students and researchers in mathematics, physics, and engineering will find this book useful.; Exercises and examples are included throughout with detailed solutions provided in the appendix.
Author : Vilmos Komornik
Publisher : Springer
ISBN 13 : 1447168119
Total Pages : 417 pages
Book Rating : 4.4/5 (471 download)
Download or read book Lectures on Functional Analysis and the Lebesgue Integral written by Vilmos Komornik and published by Springer. This book was released on 2016-06-03 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This approach leads naturally to the basic notions and theorems. Most results are illustrated by the small lp spaces. The Lebesgue integral, meanwhile, is treated via the direct approach of Frigyes Riesz, whose constructive definition of measurable functions leads to optimal, clear-cut versions of the classical theorems of Fubini-Tonelli and Radon-Nikodým. Lectures on Functional Analysis and the Lebesgue Integral presents the most important topics for students, with short, elegant proofs. The exposition style follows the Hungarian mathematical tradition of Paul Erdős and others. The order of the first two parts, functional analysis and the Lebesgue integral, may be reversed. In the third and final part they are combined to study various spaces of continuous and integrable functions. Several beautiful, but almost forgotten, classical theorems are also included. Both undergraduate and graduate students in pure and applied mathematics, physics and engineering will find this textbook useful. Only basic topological notions and results are used and various simple but pertinent examples and exercises illustrate the usefulness and optimality of most theorems. Many of these examples are new or difficult to localize in the literature, and the original sources of most notions and results are indicated to help the reader understand the genesis and development of the field.
