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| Author | : Nikolaos Katzourakis |
| Publisher | : CRC Press |
| Total Pages | : 558 |
| Release | : 2018-01-02 |
| Genre | : Mathematics |
| ISBN | : 1351765337 |
Download An Illustrative Introduction to Modern Analysis Book in PDF, ePub and Kindle
Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis. The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.
| Author | : Nikolaos Katzourakis |
| Publisher | : CRC Press |
| Total Pages | : 378 |
| Release | : 2018-01-02 |
| Genre | : Mathematics |
| ISBN | : 1351765329 |
Download An Illustrative Introduction to Modern Analysis Book in PDF, ePub and Kindle
Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis. The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.
| Author | : Kenneth Kuttler |
| Publisher | : CRC Press |
| Total Pages | : 380 |
| Release | : 1997-11-20 |
| Genre | : Mathematics |
| ISBN | : 9780849371660 |
Download Modern Analysis Book in PDF, ePub and Kindle
Modern Analysis provides coverage of real and abstract analysis, offering a sensible introduction to functional analysis as well as a thorough discussion of measure theory, Lebesgue integration, and related topics. This significant study clearly and distinctively presents the teaching and research literature of graduate analysis: Providing a fundamental, modern approach to measure theory Investigating advanced material on the Bochner integral, geometric theory, and major theorems in Fourier Analysis Rn, including the theory of singular integrals and Milhin's theorem - material that does not appear in textbooks Offering exceptionally concise and cardinal versions of all the main theorems about characteristic functions Containing an original examination of sufficient statistics, based on the general theory of Radon measures With an ambitious scope, this resource unifies various topics into one volume succinctly and completely. The contents span basic measure theory in an abstract and concrete form, material on classic linear functional analysis, probability, and some major results used in the theory of partial differential equations. Two different proofs of the central limit theorem are examined as well as a straightforward approach to conditional probability and expectation. Modern Analysis provides ample and well-constructed exercises and examples. Introductory topology is included to help the reader understand such items as the Riesz theorem, detailing its proofs and statements. This work will help readers apply measure theory to probability theory, guiding them to understand the theorems rather than merely follow directions.
| Author | : Ammar Khanfer |
| Publisher | : Springer Nature |
| Total Pages | : 377 |
| Release | : |
| Genre | : |
| ISBN | : 9819937884 |
Download Applied Functional Analysis Book in PDF, ePub and Kindle
| Author | : Ammar Khanfer |
| Publisher | : Springer Nature |
| Total Pages | : 450 |
| Release | : 2023-12-24 |
| Genre | : Mathematics |
| ISBN | : 9819930294 |
Download Fundamentals of Functional Analysis Book in PDF, ePub and Kindle
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 | : Vladimir I. Bogachev |
| Publisher | : Springer Nature |
| Total Pages | : 586 |
| Release | : 2020-02-25 |
| Genre | : Mathematics |
| ISBN | : 3030382192 |
Download Real and Functional Analysis Book in PDF, ePub and Kindle
This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.
| Author | : Kenneth Kuttler |
| Publisher | : CRC Press |
| Total Pages | : 438 |
| Release | : 2017-11-22 |
| Genre | : Mathematics |
| ISBN | : 1351359991 |
Download Modern Analysis (1997) Book in PDF, ePub and Kindle
Modern Analysis provides coverage of real and abstract analysis, offering a sensible introduction to functional analysis as well as a thorough discussion of measure theory, Lebesgue integration, and related topics. This significant study clearly and distinctively presents the teaching and research literature of graduate analysis: Providing a fundamental, modern approach to measure theory Investigating advanced material on the Bochner integral, geometric theory, and major theorems in Fourier Analysis Rn, including the theory of singular integrals and Milhin's theorem - material that does not appear in textbooks Offering exceptionally concise and cardinal versions of all the main theorems about characteristic functions Containing an original examination of sufficient statistics, based on the general theory of Radon measures With an ambitious scope, this resource unifies various topics into one volume succinctly and completely. The contents span basic measure theory in an abstract and concrete form, material on classic linear functional analysis, probability, and some major results used in the theory of partial differential equations. Two different proofs of the central limit theorem are examined as well as a straightforward approach to conditional probability and expectation. Modern Analysis provides ample and well-constructed exercises and examples. Introductory topology is included to help the reader understand such items as the Riesz theorem, detailing its proofs and statements. This work will help readers apply measure theory to probability theory, guiding them to understand the theorems rather than merely follow directions.
| Author | : John J. Benedetto |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 589 |
| Release | : 2010-01-08 |
| Genre | : Mathematics |
| ISBN | : 0817646566 |
Download Integration and Modern Analysis Book in PDF, ePub and Kindle
This textbook and treatise begins with classical real variables, develops the Lebesgue theory abstractly and for Euclidean space, and analyzes the structure of measures. The authors' vision of modern real analysis is seen in their fascinating historical commentary and perspectives with other fields. There are comprehensive treatments of the role of absolute continuity, the evolution of the Riesz representation theorem to Radon measures and distribution theory, weak convergence of measures and the Dieudonné–Grothendieck theorem, modern differentiation theory, fractals and self-similarity, rearrangements and maximal functions, and surface and Hausdorff measures. There are hundreds of illuminating exercises, and extensive, focused appendices on functional and Fourier analysis. The presentation is ideal for the classroom, self-study, or professional reference.
| Author | : Dean Corbae |
| Publisher | : Princeton University Press |
| Total Pages | : 696 |
| Release | : 2009-02-17 |
| Genre | : Business & Economics |
| ISBN | : 1400833086 |
Download An Introduction to Mathematical Analysis for Economic Theory and Econometrics Book in PDF, ePub and Kindle
Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory
| Author | : Shmuel Kantorovitz |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2023 |
| Genre | : Mathematical analysis |
| ISBN | : 9781383024432 |
Download Introduction to Modern Analysis Book in PDF, ePub and Kindle
This text is based on lectures given by the author in measure theory, functional analysis, Banach algebras, spectral theory (of bounded and unbounded operators), semigroups of operators, probability and mathematical statistics, and partial differential equations.
