We construct a calculus for generalized SG Fourier integral operators, extending known results to a broader class of symbols of SG type. In particular, we do not require that the phase functions are homogeneous. An essential ingredient in the proofs is a general criterion for asymptotic expansions within the Weyl- Hörmander calculus, which we previously proved. We also prove the L^2(R^d)-boundedness of the generalized SG Fourier integral operators having regular phase functions and uniformly bounded amplitudes.

A calculus of Fourier integral operators with inhomogeneous phase functions on R (d)

CORIASCO, Sandro;
2016

Abstract

We construct a calculus for generalized SG Fourier integral operators, extending known results to a broader class of symbols of SG type. In particular, we do not require that the phase functions are homogeneous. An essential ingredient in the proofs is a general criterion for asymptotic expansions within the Weyl- Hörmander calculus, which we previously proved. We also prove the L^2(R^d)-boundedness of the generalized SG Fourier integral operators having regular phase functions and uniformly bounded amplitudes.
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http://www.springer.com/mathematics/journal/13226
Fourier Integral Operator, Weyl-Hörmander calculus, micro-local analysis
S. Coriasco; J. Toft
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/151605
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