PreprintCC BY 4.0arXiv
Stability of concentration in the Paley-Wiener space
Abstract
We prove stability of concentration in the Paley-Wiener space for each fixed time-bandwidth product. The concentration deficit controls the squared L2(ℝ)-distance from a translated first prolate spheroidal wave function and the squared normalized symmetric difference from an interval at the same center. The obtained exponent for the function distance is optimal. The main idea is the introduction of the set discrepancy weighted by the best optimizers in place of the symmetric difference. The proof then combines elementary Hilbert space arguments with classical properties of the prolate spheroidal wave functions.
Related
- Stochastic Euler Products in the Paley-Wiener Space
- Helson Inequality, Hankel Operators, and Weak Factorization on Paley-Wiener spaces of Convex Domains
- A trace Paley-Wiener theorem for GLn(F)backslash GLn(E), with E/F a quadratic extension of non-Archimedean local fields
- The zeros of point evaluation extremals in Paley-Wiener spaces
- Dynamical Sampling in Graph Paley--Wiener Spaces
BibTeX
@misc{zelent2026stability,
title = {{Stability of concentration in the Paley-Wiener space}},
author = {Denis Zelent},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01299},
eprint = {2610.01299},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01299},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stability of concentration in the Paley-Wiener space
AU - Denis Zelent
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01299
UR - https://arxiv.org/abs/2610.01299
AB - We prove stability of concentration in the Paley-Wiener space for each fixed time-bandwidth product. The concentration deficit controls the squared L^2(ℝ)-distance from a translated first prolate spheroidal wave function and the squared normalized symmetric difference from an interval at the same center. The obtained exponent for the function distance is optimal. The main idea is the introduction of the set discrepancy weighted by the best optimizers in place of the symmetric difference. The proof then combines elementary Hilbert space arguments with classical properties of the prolate spheroidal wave functions.
ER -