Band-limited maximizers for a Fourier extension inequality on the circle, II

TL;DR

This paper proves that within a specific class of functions on the circle, constant functions uniquely maximize the endpoint Tomas-Stein inequality, highlighting their optimality among band-limited functions.

Contribution

It establishes the uniqueness of constant functions as maximizers for the endpoint Tomas-Stein inequality among band-limited functions on the circle.

Findings

Constant functions are the unique maximizers among band-limited functions.

The result applies to functions with Fourier modes up to degree 120.

It confirms the optimality of constant functions for this inequality.

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.