Perspectives in Analysis

1. Front Matter

   Pages I-XIV

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2. The Rosetta Stone of L-functions

   • Enrico Bombieri

   Pages 1-15

3. New Encounters in Combinatorial Number Theory: From the Kakeya Problem to Cryptography

   • J. Bourgain

   Pages 17-26

4. Perspectives and Challenges to Harmonic Analysis and Geometry in High Dimensions: Geometric Diffusions as a Tool for Harmonic Analysis and Structure Definition of Data

   • R. R. Coifman

   Pages 27-35

5. Open Questions on the Mumford-Shah Functional

   • Guy David

   Pages 37-49

6. Multi-scale Modeling

   • Björn Engquist

   Pages 51-61

7. Mass in Quantum Yang-Mills Theory (Comment on a Clay Millennium Problem)

   • L. D. Faddeev

   Pages 63-72

8. On Scaling Properties of Harmonic Measure

   • Peter W. Jones

   Pages 73-81

9. The Heritage of Fourier

   • Jean-Pierre Kahane

   Pages 83-95

10. The Quantum-Mechanical Many-Body Problem: The Bose Gas

    • Elliott H. Lieb, Robert Seiringer, Jan Philip Solovej, Jakob Yngvason

    Pages 97-183

11. Meromorphic Inner Functions, Toeplitz Kernels and the Uncertainty Principle

    • N. Makarov, A. Poltoratski

    Pages 185-252

12. Heat Measures and Unitarizing Measures for Berezinian Representations on the Space of Univalent Functions in the Unit Disk

    • Paul Malliavin

    Pages 253-268

13. On Local and Global Existence and Uniqueness of Solutions of the 3D Navier—Stokes System on ℝ3

    • Ya. G. Sinai

    Pages 269-281

14. Analysis on Lie Groups: An Overview of Some Recent Developments and Future Prospects

    • Nicholas Th. Varopoulos

    Pages 283-293

15. Encounters with Science: Dialogues in Five Parts

    • Lars Gårding

    Pages 295-376

16. Back Matter

    Pages 377-378

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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.

• Carleson Measure
• Harmonic Analysis
• Lennart Carleson
• calculus
• differential equation
• measure

• Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden

  Michael Benedicks, Stanislav Smirnov

• Department of Mathematics, Yale University, New Haven, USA

  Peter W. Jones

• Section de Mathématiques, Université de Genève, Genève 4, Switzerland

  Stanislav Smirnov

• Department of Mathematics, University of Groningen, Groningen, The Netherlands

  Björn Winckler

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