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Dispersive type estimates for fourier integrals and applications to hyperbolic systems
In this note we announce dispersive estimates for Fourier integrals
with parameter-dependent phase functions in terms of geometric quantities
of associated families of Fresnel surfaces. The results are based on a multidimensional van der Corput lemma due to the rst author.
Applications to dispersive estimates for hyperbolic systems and scalar higher
order hyperbolic equations are also discussed.