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Advances in Phase Space Analysis of Partial Differential Equations

In Honor of Ferruccio Colombini's 60th Birthday

  • Book
  • © 2009

Overview

Editors:
  1. Antonio Bove

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

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  2. Daniele Del Santo

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

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  3. M.K. Venkatesha Murthy

    1. Dipto. Matematica, Università Pisa, Pisa, Italy

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  • Provides both surveys and recent advances in phase space analysis for pdes
  • Distinguished mathematicians address current work of importance
  • Includes supplementary material: sn.pub/extras

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 78)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  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
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Keywords

About this book

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.

Editors and Affiliations

  • 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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