Twelve Landmarks of Twentieth-Century Analysis

This book combines rigorous proofs with commentary on the underlying ideas to provide a rich insight into these mathematical landmarks.

D. Choimet (Author), H. Queffélec (Author)

9781107059450, Cambridge University Press

Hardback, published 16 July 2015

521 pages, 25 b/w illus. 153 exercises
23.5 x 16 x 3.2 cm, 0.85 kg

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.

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 ?0
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.

Subject Areas: History of mathematics [PBX], Real analysis, real variables [PBKB], Calculus & mathematical analysis [PBK], Number theory [PBH]