On nearly radial product functions

Michael Christ

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arXiv · 1506.00155

On nearly radial product functions

Michael Christ

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Abstract

If $f\in L^2(R^d)$ and if the function $f(x)f(y)$ is close in $L^2(R^{2d})$ norm to a radially symmetric function of $(x,y)$ then $f$ is close in $L^2$ norm to a centered Gaussian function. This is proved in a quantitative form with the optimal exponent measuring closeness.

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Michael Christ. 2015-05-30. On nearly radial product functions. https://arxiv.org/abs/1506.00155

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