Perspectives in Analysis: Essays in Honor of Lennart Carleson's 75th Birthday (Mathematical Physics Studies Book 27)

The purpose of the essays collected in this volume is to consider the future of analysis and related areas of physics. It is published in honor of Lennart Carleson, who has devoted much of his career to broadening the scope of harmonic analysis. Written by leading mathematicians and mathematical physicists, the articles should inspire new avenues of research. The collection shows the impressive relationship between physical intuition and mathematical analysis. These essays give confidence that the meeting ground between these areas of mathematics and physics will only grow more fertile in the future. The Conference “Perspectives in Analysis” was held during May 26–28, 2003 at the Royal Institute of Technology in Stockholm, Sweden. The purpose of the conference was to consider the future of analysis along with its relations to other areas of mathematics and physics, and to celebrate the seventy-?fth birthday of Lennart Carleson. The scienti?c theme was one with which the name of Lennart Carleson has been associated for over ?fty years. His modus operandi has long been to carry out a twofold approach to the selection of research problems. First one should look for promising new areas of ana- sis, especially those having close contact with physically oriented problems of geometric character. The second step is to select a core set of problems that require new techniques for their resolutions. After making a central contri- tion, Lennart would usually move on to a new area, though he might return to the topic of his previous work if new techniques were developed that could break old mathematical log jams. Lennart’s operating approach is based on fundamental realities of modern mathematics as well as his own inner c- victions. Here we ?rst refer to an empirical fact of mathematical research: All topics have a ?nite half-life, with ?fteen years being an upper bound for most areas. After that time it is usually a good idea to move on to so- thing new. The Rosetta Stone of L -functions....Pages 1-15 New Encounters in Combinatorial Number Theory: From the Kakeya Problem to Cryptography....Pages 17-26 Perspectives and Challenges to Harmonic Analysis and Geometry in High Dimensions: Geometric Diffusions as a Tool for Harmonic Analysis and Structure Definition of Data....Pages 27-35 Open Questions on the Mumford-Shah Functional....Pages 37-49 Multi-scale Modeling....Pages 51-61 Mass in Quantum Yang-Mills Theory (Comment on a Clay Millennium Problem)....Pages 63-72 On Scaling Properties of Harmonic Measure....Pages 73-81 The Heritage of Fourier....Pages 83-95 The Quantum-Mechanical Many-Body Problem: The Bose Gas....Pages 97-183 Meromorphic Inner Functions, Toeplitz Kernels and the Uncertainty Principle....Pages 185-252 Heat Measures and Unitarizing Measures for Berezinian Representations on the Space of Univalent Functions in the Unit Disk....Pages 253-268 On Local and Global Existence and Uniqueness of Solutions of the 3D Navier—Stokes System on R 3 ....Pages 269-281 Analysis on Lie Groups: An Overview of Some Recent Developments and Future Prospects....Pages 283-293 Encounters with Science: Dialogues in Five Parts....Pages 295-376 Considers the future of analysis and related areas of physics. This collection of essays is published in honor of Lennart Carleson, who has devoted his career to broadening the scope of harmonic analysis. Written by leading mathematicians and mathematical physicists, it shows the relationship between physical intuition and mathematical analysis DVD-ROM contains videos of the talks by the authors