Band-limited maximizers for a Fourier extension inequality on the circle
Diogo Oliveira e Silva, Christoph Thiele, Pavel Zorin-Kranich
TL;DR
This paper proves that within functions limited to Fourier modes up to degree 30, constant functions uniquely maximize the endpoint Tomas-Stein inequality on the circle.
Contribution
It establishes the uniqueness of constant functions as maximizers for a specific Fourier extension inequality on the circle within a certain Fourier mode range.
Findings
Constant functions are the unique maximizers among functions with Fourier modes up to 30.
The result characterizes extremizers for the endpoint Tomas-Stein inequality on the circle.
The proof is restricted to functions with Fourier modes up to degree 30.
Abstract
Among the class of functions with Fourier modes up to degree 30, constant functions are the unique real-valued maximizers for the endpoint Tomas-Stein inequality on the circle.
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