Topics In Banach Space Integration

Author : ?tefan Schwabik
Publisher : World Scientific
ISBN 13 : 9812564284
Total Pages : 313 pages
Book Rating : 4.83/5 ( download)

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Download or read book Topics in Banach Space Integration written by ?tefan Schwabik and published by World Scientific. This book was released on 2005 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relatively new concepts of the Henstock-Kurzweil and McShane integrals based on Riemann type sums are an interesting challenge in the study of integration of Banach space-valued functions. This timely book presents an overview of the concepts developed and results achieved during the past 15 years. The Henstock-Kurzweil and McShane integrals play the central role in the book. Various forms of the integration are introduced and compared from the viewpoint of their generality. Functional analysis is the main tool for presenting the theory of summation gauge integrals.

Author : Guoju Ye
Publisher : World Scientific
ISBN 13 : 9814479683
Total Pages : 313 pages
Book Rating : 4.84/5 ( download)

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Download or read book Topics In Banach Space Integration written by Guoju Ye and published by World Scientific. This book was released on 2005-08-16 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relatively new concepts of the Henstock-Kurzweil and McShane integrals based on Riemann type sums are an interesting challenge in the study of integration of Banach space-valued functions. This timely book presents an overview of the concepts developed and results achieved during the past 15 years. The Henstock-Kurzweil and McShane integrals play the central role in the book. Various forms of the integration are introduced and compared from the viewpoint of their generality. Functional analysis is the main tool for presenting the theory of summation gauge integrals.

Author : Fernando Albiac
Publisher : Springer
ISBN 13 : 3319315579
Total Pages : 508 pages
Book Rating : 4.77/5 ( download)

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Download or read book Topics in Banach Space Theory written by Fernando Albiac and published by Springer. This book was released on 2016-07-19 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book...succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly... It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments... I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book..."—Gilles Godefroy, Mathematical Reviews

Author : Charles W Swartz
Publisher : World Scientific
ISBN 13 : 9814502510
Total Pages : 294 pages
Book Rating : 4.11/5 ( download)

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Download or read book Measure, Integration And Function Spaces written by Charles W Swartz and published by World Scientific. This book was released on 1994-02-21 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text contains a basic introduction to the abstract measure theory and the Lebesgue integral. Most of the standard topics in the measure and integration theory are discussed. In addition, topics on the Hewitt-Yosida decomposition, the Nikodym and Vitali-Hahn-Saks theorems and material on finitely additive set functions not contained in standard texts are explored. There is an introductory section on functional analysis, including the three basic principles, which is used to discuss many of the classic Banach spaces of functions and their duals. There is also a chapter on Hilbert space and the Fourier transform.

Author : Robert E. Megginson
Publisher : Springer Science & Business Media
ISBN 13 : 1461206030
Total Pages : 613 pages
Book Rating : 4.33/5 ( download)

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Download or read book An Introduction to Banach Space Theory written by Robert E. Megginson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.

Author : J. Diestel
Publisher : Springer
ISBN 13 : 3540379134
Total Pages : 298 pages
Book Rating : 4.33/5 ( download)

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Download or read book Geometry of Banach Spaces - Selected Topics written by J. Diestel and published by Springer. This book was released on 2006-11-14 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Ng Wee Leng
Publisher : World Scientific
ISBN 13 : 9813221984
Total Pages : 248 pages
Book Rating : 4.87/5 ( download)

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Download or read book Nonabsolute Integration On Measure Spaces written by Ng Wee Leng and published by World Scientific. This book was released on 2017-10-20 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers to the reader a self-contained treatment and systematic exposition of the real-valued theory of a nonabsolute integral on measure spaces. It is an introductory textbook to Henstock–Kurzweil type integrals defined on abstract spaces. It contains both classical and original results that are accessible to a large class of readers. It is widely acknowledged that the biggest difficulty in defining a Henstock–Kurzweil integral beyond Euclidean spaces is the definition of a set of measurable sets which will play the role of "intervals" in the abstract setting. In this book the author shows a creative and innovative way of defining "intervals" in measure spaces, and prove many interesting and important results including the well-known Radon–Nikodým theorem. Contents: A Nonabsolute Integral on Measure Spaces: PreliminariesExistence of a Division and the H-IntegralSimple Properties of the H-IntegralThe Absolute H-Integral and the McShane-Type Integrals: The Absolute H-Integral and the M-IntegralThe H-Integral and the Lebesgue IntegralThe Davies Inetgral and the Davies-McShane IntegralFurther Results of the H-Integral: A Necessary and Sufficient Condition for H-IntegrabilityGeneralised Absolute Continuity and EquiintegrabilityThe Controlled Convergence TheoremThe Radon–Nikodým Theorem for the H-integral: The Main TheoremDescriptive Definition of H-integralHenstock Integration in the Euclidean SpaceHarnack Extension and Convergence Theorems for the H-Integral: The H-Integral on Metric SpacesHarnack Extension for the H-IntegralThe Category ArgumentAn Improved Version of the Controlled Convergence Theorem Readership: Graduate students and researchers interested in analysis. Keywords: Henstock-Kurzweil Type Integral;Generalized Intervals;Nonabsolute Integration;Measure Spaces;Locally Compact Hausdorff Space;Radon-Nikodym Theorem;Controlled Convergence Theorem;Harnack ExtensionReview: Key Features: To our knowledge there is no book on integration theory whose setting is measure spaces with a topological structureThe theory is developed in a progressive and elementary manner in that the fundamental properties are first established before further results are proved. That way, even though the setting is abstract, this book is accessible to any undergraduate who has done an advanced calculus courseThe key idea behind each original concept is always explained in an intuitive manner before the formal definitions and results are presented in detail

Author : Tuo Yeong Lee
Publisher : World Scientific
ISBN 13 : 9814324582
Total Pages : 325 pages
Book Rating : 4.88/5 ( download)

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Download or read book Henstock-Kurzweil Integration on Euclidean Spaces written by Tuo Yeong Lee and published by World Scientific. This book was released on 2011 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Henstock?Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock?Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus.

Author : Martin Vaeth
Publisher : World Scientific Publishing Company
ISBN 13 : 9813106034
Total Pages : 288 pages
Book Rating : 4.31/5 ( download)

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Download or read book Integration Theory - A Second Course written by Martin Vaeth and published by World Scientific Publishing Company. This book was released on 2002-08-15 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a general approach to integration theory, as well as some advanced topics. It includes some new results, but is also a self-contained introduction suitable for a graduate student doing self-study or for an advanced course on integration theory.The book is divided into two parts. In the first part, integration theory is developed from the start in a general setting and immediately for vector-valued functions. This material can hardly be found in other textbooks. The second part covers various topics related to integration theory, such as spaces of measurable functions, convolutions, famous paradoxes, and extensions of formulae from elementary calculus to the setting of the Lebesgue integral.

Author : Siegfried Carl
Publisher : Springer Science & Business Media
ISBN 13 : 1441975853
Total Pages : 482 pages
Book Rating : 4.50/5 ( download)

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Download or read book Fixed Point Theory in Ordered Sets and Applications written by Siegfried Carl and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a unified and comprehensive treatment of an order-theoretic fixed point theory in partially ordered sets and its various useful interactions with topological structures. The material progresses systematically, by presenting the preliminaries before moving to more advanced topics. In the treatment of the applications a wide range of mathematical theories and methods from nonlinear analysis and integration theory are applied; an outline of which has been given an appendix chapter to make the book self-contained. Graduate students and researchers in nonlinear analysis, pure and applied mathematics, game theory and mathematical economics will find this book useful.