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arXiv · 1701.06099

A multilinear Fourier extension identity on $\mathbb{R}^n$

Jonathan Bennett·Marina Iliopoulou
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Abstract

We prove an elementary multilinear identity for the Fourier extension operator on $\mathbb{R}^n$, 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 Schr\"odinger 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.

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Jonathan Bennett, Marina Iliopoulou. 2017-01-21. A multilinear Fourier extension identity on $\mathbb{R}^n$. https://arxiv.org/abs/1701.06099

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