Band-Limited Maximizers for a Fourier Extension Inequality on the Circle, II

Abstract

Among the class of functions on the circle with Fourier modes up to degree 120, constant functions are the unique real-valued maximizers for the endpoint Tomas-Stein inequality.

Keywords:

• Tomas-Stein inequality
• harmonic analysis
• functional analysis

Acknowledgments

The main calculations described in this article were performed using the supercomputing facilities of Fraunhofer SCAI. The authors also gratefully acknowledge the comments and suggestions of the anonymous reviewers, and in particular their detection of several small errors.

Notes

1 See https://arxiv.org/abs/2002.05118.

2 During the preparation of the final version of this article, the authors became aware of a minor but nonnegligible error in previous preprint versions, namely that an incorrect value of T was used in the numerical calculation of the tail approximation ${\tilde{I}}_{\mathbf{k}}^{T,\infty }$ in (3). The error has been corrected, and all values, plots, etc. have been recalculated and updated accordingly.

Additional information

Funding

The authors acknowledge support by the Deutsche Forschungsgemeinschaft through the Hausdorff Center for Mathematics (DFG Projektnummer 390685813) and the Collaborative Research Center 1060 (DFG Projektnummer 211504053).