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      Book

      Principles of Analysis
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      Book

      Principles of Analysis

      DOI link for Principles of Analysis

      Principles of Analysis book

      Measure, Integration, Functional Analysis, and Applications

      Principles of Analysis

      DOI link for Principles of Analysis

      Principles of Analysis book

      Measure, Integration, Functional Analysis, and Applications
      ByHugo D. Junghenn
      Edition 1st Edition
      First Published 2017
      eBook Published 15 November 2017
      Pub. Location New York
      Imprint Chapman and Hall/CRC
      DOI https://doi.org/10.1201/9781315151601
      Pages 540
      eBook ISBN 9781315151601
      Subjects Engineering & Technology, Mathematics & Statistics
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      Junghenn, H.D. (2017). Principles of Analysis: Measure, Integration, Functional Analysis, and Applications (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9781315151601

      ABSTRACT

      Principles of Analysis: Measure, Integration, Functional Analysis, and Applications prepares readers for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level. The book also helps them prepare for qualifying exams in real analysis. It is designed so that the reader or instructor may select topics suitable to their needs. The author presents the text in a clear and straightforward manner for the readers’ benefit. At the same time, the text is a thorough and rigorous examination of the essentials of measure, integration and functional analysis.

      The book includes a wide variety of detailed topics and serves as a valuable reference and as an efficient and streamlined examination of advanced real analysis. The text is divided into four distinct sections: Part I develops the general theory of Lebesgue integration; Part II is organized as a course in functional analysis; Part III discusses various advanced topics, building on material covered in the previous parts; Part IV includes two appendices with proofs of the change of the variable theorem and a joint continuity theorem. Additionally, the theory of metric spaces and of general topological spaces are covered in detail in a preliminary chapter .

      Features:

      • Contains direct and concise proofs with attention to detail
      • Features a substantial variety of interesting and nontrivial examples
      • Includes nearly 700 exercises ranging from routine to challenging with hints for the more difficult exercises
      • Provides an eclectic set of special topics and applications

      About the Author:

      Hugo D. Junghenn is a professor of mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including Option Valuation: A First Course in Financial Mathematics and A Course in Real Analysis. His research interests include functional analysis, semigroups, and probability.

      TABLE OF CONTENTS

      chapter |40 pages

      Preliminaries

      part I|155 pages

      Measure and Integration

      chapter 1|31 pages

      Measurable Sets

      chapter 2|14 pages

      Measurable Functions

      chapter 3|34 pages

      Integration

      chapter 4|16 pages

      L p $ {\boldsymbol{L}}^{\boldsymbol{p}} $ Spaces

      chapter 5|29 pages

      Differentiation

      chapter 6|12 pages

      Fourier Analysis on R d $ \mathbb R ^d $

      chapter 7|15 pages

      Measures on Locally Compact Spaces

      part II|170 pages

      Functional Analysis

      chapter 8|42 pages

      Banach Spaces

      chapter 9|15 pages

      Locally Convex Spaces

      chapter 10|15 pages

      Weak Topologies on Normed Spaces

      chapter 11|16 pages

      Hilbert Spaces

      chapter 12|26 pages

      Operator Theory

      chapter 13|26 pages

      Banach Algebras

      chapter 14|26 pages

      Miscellaneous Topics

      part III|125 pages

      Applications

      chapter 15|16 pages

      Distributions

      chapter 16|38 pages

      Analysis on Locally Compact Groups

      chapter 17|20 pages

      Analysis on Semigroups

      chapter 18|49 pages

      Probability Theory

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