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Archiv der Mathematik

, Volume 72, Issue 1, pp 68–76 | Cite as

Analytic Fourier integral operators, Monge-Ampère equation and holomorphic factorization

  • Michael Ruzhansky

Abstract.

We will show that the factorization condition for the Fourier integral operators \(I_\rho ^\mu (X,Y;\it\Lambda )\) leads to a parametrized parabolic Monge-Ampère equation. For an analytic operator, the fibration by the kernels of the Hessian of phase function is shown to be analytic in a number of cases, by considering a more general continuation problem for the level sets of a holomorphic mapping. The results are applied to obtain L p -continuity for translation invariant operators in \({\Bbb R}^n\) with \(n\leq 4\) and for arbitrary \({\Bbb R}^n\) with \(d\pi _{X\times Y}|_\Lambda \leq n+2\).

Keywords

Analytic Operator Integral Operator Holomorphic Mapping Factorization Condition Phase Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • Michael Ruzhansky
    • 1
  1. 1.Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USAUS

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