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Informationen zum Autor 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. Klappentext This book combines rigorous proofs with commentary on the underlying ideas to provide a rich insight into these mathematical landmarks. Zusammenfassung The authors combine rigorous mathematical proofs with commentary on the underlying ideas to provide a rich insight into some of the most profound results of twentieth-century analysis. This English edition contains a new chapter on partitions and significantly expands the existing chapter on the Corona problem. Inhaltsverzeichnis 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....
