A multilinear Fourier extension identity on Rn

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Colleges, School and Institutes

Abstract

We prove an elementary multilinear identity for the Fourier extension operator on Rn, generalising to higher dimensions the classical bilinear extension identity in the plane. In the particular case of the extension operator associated with the paraboloid, this provides a higher dimensional extension of a well-known identity of Ozawa and Tsutsumi for solutions to the free time-dependent Schrödinger equation. We conclude with a similar treatment of more general oscillatory integral operators whose phase functions collectively satisfy a natural multilinear transversality condition. The perspective we present has its origins in work of Drury.

Details

Original languageEnglish
Pages (from-to)1089-1108
JournalMathematical Research Letters
Volume25
Issue number4
Publication statusPublished - 16 Nov 2018

Keywords

  • math.CA