On extremisers to a bilinear Strichartz inequality

TL;DR

This paper identifies Gaussian functions as the extremisers for a bilinear Strichartz inequality, demonstrating their uniqueness up to symmetry transformations, thus advancing understanding of extremal functions in harmonic analysis.

Contribution

The paper proves that Gaussian functions are the unique extremisers for a specific bilinear Strichartz inequality, up to symmetry.

Findings

Gaussian functions are extremisers

Extremisers are unique up to symmetry

Provides insight into extremal functions in harmonic analysis

Abstract

In this note, we show that a pair of Gaussian functions are extremisers to a bilinear Strichartz inequality, and unique up to the symmetry group of the inequality.