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A Class of Fourier Integral Operators on Manifolds with Boundary

  • Ubertino BattistiEmail author
  • Sandro Coriasco
  • Elmar Schrohe
Part of the Operator Theory: Advances and Applications book series (OT, volume 245)

Abstract

We study a class of Fourier integral operators on compact manifolds with boundary X and Y , associated with a natural class of symplectomorphisms \(\mathcal{X} :\;T^{*}Y \; \backslash \;0\rightarrow\;T^{*}X\; \backslash \;0\), namely, those which preserve the boundary. A calculus of Boutet de Monvel’s type can be defined for such Fourier integral operators, and appropriate continuity properties established. One of the key features of this calculus is that the local representations of these operators are given by operator-valued symbols acting on Schwartz functions or temperate distributions. Here we focus on properties of the corresponding local phase functions, which allow to prove this result in a rather straightforward way.

Keywords

Fourier integral operator manifold with boundary boundary-preserving symplectomorphism 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ubertino Battisti
    • 1
    Email author
  • Sandro Coriasco
    • 1
  • Elmar Schrohe
    • 2
  1. 1.Dipartimento di MatematicaUniversità di TorinoTorinoItaly
  2. 2.Institut für AnalysisLeibniz Universität HannoverHannoverGermany

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