Phase Space Localization of Riesz bases for L^2(R^d)

TL;DR

This paper establishes a strong uncertainty principle for Riesz bases in L^2(R^d) and demonstrates that Bourgain's orthonormal basis achieves optimal phase-space localization, advancing understanding of basis localization properties.

Contribution

It introduces a strong uncertainty principle for Riesz bases and proves Bourgain's basis has optimal phase-space localization, a novel result in basis theory.

Findings

Proves a strong uncertainty principle for Riesz bases.

Shows Bourgain's basis has optimal phase-space localization.

Abstract

We prove a strong uncertainty principle for Riesz bases in L^2(R^d) and show that the orthonormal basis constructed by Bourgain possesses the optimal phase-space localization.