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Article Contents

# 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.
Mathematics Subject Classification: Primary: 35B45; Secondary: 35L05, 35L45.

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