Twelve Landmarks of Twentieth-Century Analysis

D. Choimet, H. Queffélec (Université de Lille)

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English

Cambridge University Press
16 July 2015

Number theory; Calculus & mathematical analysis; Real analysis, real variables; History of mathematics

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.

By: D. Choimet, H. Queffélec (Université de Lille)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 230mm, Width: 150mm, Spine: 28mm
Weight: 720g
ISBN: 9781107650343
ISBN 10: 1107650348
Pages: 546
Publication Date: 16 July 2015
Audience: Professional and scholarly , Professional and scholarly , Undergraduate , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

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 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.