Work

Smallest Singular Value Estimates for Nonuniform Fourier Matrices via Periodic Nonuniform Sampling

Year: 2026

Type: preprint

Abstract: We study the smallest singular value of nonuniform Fourier matrices in two settings: clustered nodes and perturbations of an equispaced grid. By reducing the problem to spectral norm estimates for periodic nonuniform interpolation matrices, we obtain nearly optimal bounds in both cases. For clustered nodes, we derive the first local separation condition in which each required gap depends only on the sizes of the two neighboring clusters. For perturbations with the bound \(1/4\leq L<1/2\), our result confirms the conjecture of Austin and Trefethen on the \(2\)-norm Lebesgue constant up to a logarithmic factor.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.21960

Authors: Chen, Liang, Lin, Rongrong, Zhang, Haizhang

Institutions: Guangdong University of Technology, Jiujiang University, Sun Yat-sen University

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

OpenAlex ID: W7204173650

Cites: 2

Cited by:

Related to: 10