Advances in Phase Space Analysis of Partial Differential Equations

1. Front Matter

   Pages i-xiv

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2. Tangent Halfspaces to Sets of Finite Perimeter in Carnot Groups

   • Luigi Ambrosio

   Pages 1-16

3. The Heat Kernel and Frequency Localized Functions on the Heisenberg Group

   • Hajer Bahouri, Isabelle Gallagher

   Pages 17-35

4. A Generalization of the Rudin–Carleson Theorem

   • Shiferaw Berhanu, Jorge Hounie

   Pages 37-57

5. Evolution Equations and Generalized Fourier Integral Operators

   • Jean-Michel Bony

   Pages 59-72

6. The Solvability and Subellipticity of Systems of Pseudodifferential Operators

   • Nils Dencker

   Pages 73-94

7. Uniform Exponential Decay for Viscous Damped Systems*

   • Sylvain Ervedoza, Enrique Zuazua

   Pages 95-112

8. The Hyperbolic Symmetrizer: Theory and Applications

   • Enrico Jannelli

   Pages 113-139

9. Time Global Solutions to the Cauchy Problem for Multidimensional Kirchhoff Equations

   • Kunihiko Kajitani

   Pages 141-153

10. The Order of Accuracy of Quadrature Formulae for Periodic Functions

    • Alexander Kurganov, Jeffrey Rauch

    Pages 155-159

11. A Note on the Oseen Kernels

    • Nicolas Lerner

    Pages 161-170

12. Instability Behavior and Loss of Regularity

    • Xiaojun Lu, Michael Reissig

    Pages 171-200

13. Decay Estimates for Variable Coefficient Wave Equations in Exterior Domains

    • Jason Metcalfe, Daniel Tataru

    Pages 201-216

14. On Gevrey Well-Posedness of the Cauchy Problem for Some Noneffectively Hyperbolic Operators

    • Tatsuo Nishitani

    Pages 217-233

15. Singularities of the Scattering Kernel Related to Trapping Rays

    • Vesselin Petkov, Luchezar Stoyanov

    Pages 235-251

16. Analytic Hypoellipticity for a Sum of Squares of Vector Fields in ℝ3 Whose Poisson Stratification Consists of a Single Symplectic Stratum of Codimension Four

    • David S. Tartakoff

    Pages 253-261

17. Multidimensional Soliton Integrodifferential Systems

    • François Treves *

    Pages 263-289

18. Selected lectures in Microlocal Analysis

    • Giuseppe Zampieri

    Pages 291-301

The present volume is a collection of papers mainly concerning Phase Space Analysis,alsoknownasMicrolocal Analysis,anditsapplicationstothetheory of Partial Di?erential Equations (PDEs). The basic idea behind this theory, at the crossing of harmonic analysis, functional analysis, quantum mechanics and algebraic analysis, is that many phenomena depend on both position and frequency (or wave numbers, or momentum) and therefore must be understood and described in the phase space. Including time and its dual variable, the energy, leads to the spa- time phase space. From this perspective major progress has been achieved in the analysis of PDEs over the last forty years, based on the development of powerful tools of microlocal analysis. A number of the following papers, all written by leading experts in their respective ?elds, are expanded versions of talks given at a meeting held in October 2007 at the Certosa di Pontignano, a former 1400 cloister sprawling on the hills surrounding Siena. The Siena workshop was in honor of Ferruccio Colombini on the occasion of his 60th birthday and it is our pleasure to dedicate to him this volume, to which a number of friends and collaborators promptly manifested their willingness to contribute. In this sense the present volume can be seen as a scienti?c portrait of Ferruccio. Many people deserve our gratitude. We would like to thank all the c- tributors as well as the people who took part in the workshop, who made a lively mathematical attendance.

• Analysis
• analytic hypoellipticity
• hyperbolic equation
• hyperbolic equations
• local solvability
• operator
• subellipticity
• wave equation
• partial differential equations

• Dipto. Matematica, Università di Bologna, Bologna, Italy

  Antonio Bove

• Dipto. Scienze Matematiche, Università di Trieste, Trieste, Italy

  Daniele Del Santo

• Dipto. Matematica, Università Pisa, Pisa, Italy

  M.K. Venkatesha Murthy

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