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Twelve Landmarks of Twentieth-Century Analysis

Gilles Godefroy
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  • Date Published: July 2015
  • availability: Available
  • format: Paperback
  • isbn: 9781107650343

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  • The striking theorems showcased in this book are among the most profound results of twentieth-century analysis. The authors' original approach combines rigorous mathematical proofs with commentary on the underlying ideas to provide a rich insight into these landmarks in mathematics. Results ranging from the proof of Littlewood's conjecture to the Banach–Tarski paradox have been selected for their mathematical beauty as well as educative value and historical role. Placing each theorem in historical perspective, the authors paint a coherent picture of modern analysis and its development, whilst maintaining mathematical rigour with the provision of complete proofs, alternative proofs, worked examples, and more than 150 exercises and solution hints. This edition extends the original French edition of 2009 with a new chapter on partitions, including the Hardy–Ramanujan theorem, and a significant expansion of the existing chapter on the Corona problem.

    • Showcases the work of Littlewood, Riemann, Hadamard, Wiener and others
    • This first English edition contains a brand new chapter on partitions, including the Hardy–Ramanujan theorem and its improvement by Rademacher
    • Provides more than 150 exercises with hints on how to solve them
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    Product details

    • Date Published: July 2015
    • format: Paperback
    • isbn: 9781107650343
    • dimensions: 230 x 150 x 28 mm
    • weight: 0.7kg
    • contains: 25 b/w illus. 153 exercises
    • availability: Available
  • Table of Contents

    Foreword Gilles Godefroy
    Preface
    1. The Littlewood Tauberian theorem
    2. The Wiener Tauberian theorem
    3. The Newman Tauberian theorem
    4. Generic properties of derivative functions
    5. Probability theory and existence theorems
    6. The Hausdorff–Banach–Tarski paradoxes
    7. Riemann's 'other' function
    8. Partitio Numerorum
    9. The approximate functional equation of θ0
    10. The Littlewood conjecture
    11. Banach algebras
    12. The Carleson corona theorem
    13. The problem of complementation in Banach spaces
    14. Hints for solutions
    References
    Notations
    Index.

  • Authors

    D. Choimet, Lycée du Parc, Lyon
    D. Choimet has spent all of his academic career in the French 'Classes Préparatoires', an intensive two-year undergraduate programme leading to a nation-wide competitive examination for enrolment in one of the 'Grandes Écoles'. He currently teaches at the Lycée du Parc in Lyon, preparing students for the Écoles Normales Supérieures, the École Polytechnique and many graduate engineering schools. Choimet is also a member of the jury of the 'Agrégation', a competitive examination leading to professorship positions.

    H. Queffélec, Université de Lille
    H. Queffélec shared his academic career between the universities of Paris-Sud and later Lille, where he is now an Emeritus Professor. He has written around fourty research papers in harmonic analysis and related probabilistic or topological methods, as well as in number theory (Dirichlet series) and operator theory, more specifically, composition operators and their approximation numbers. He has also written five textbooks and a research book on Banach spaces and Probabilistic methods (in collaboration with D. Li). Queffélec has served on the committees for selecting secondary school Professors (Agrégation), and for hiring University researchers. He was also a member of the CNU (National Council of Universities in France) which deals with the promotion of University members.

    Contributors

    Gilles Godefroy

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