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.
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
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 in (3). The error has been corrected, and all values, plots, etc. have been recalculated and updated accordingly.