Fourier restriction estimates on quantum Euclidean spaces

TL;DR

This paper explores Fourier restriction phenomena on quantum Euclidean spaces, establishing analogues of classical restriction theorems, thus extending harmonic analysis into non-commutative geometric settings.

Contribution

It introduces the study of Fourier restriction estimates on quantum Euclidean spaces and proves key theorems analogous to classical results.

Findings

Established the Tomas-Stein restriction theorem analogue.

Proved the two-dimensional full restriction theorem.

Extended harmonic analysis techniques to quantum spaces.

Abstract

In this paper, we initiate the study of the Fourier restriction phenomena on quantum Euclidean spaces, and establish the analogues of the Tomas-Stein restriction theorem and the two-dimensional full restriction theorem.