Year: 2026
Type: preprint
Abstract: We proved recently that there are no unconditional Schauder frames of exponentials in the space $L^p(Ω)$, $1 \le p < 2$, for any set $Ω\subset \mathbb{R}^d$ of finite measure. For $p > 2$, we proved that the same holds provided that $Ω$ has nonempty interior, but the general case remained open. In this note we close this gap, i.e., we establish that exponentials cannot form an unconditional Schauder frame in $L^p(Ω)$, $p \ne 2$, without any additional assumptions on the set $Ω$ of finite measure other than measurability.
Source: arXiv (Cornell University)
Authors: Lev, Nir, Tselishchev, Anton
Institutions: Bar-Ilan University, Steklov Mathematical Institute
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Israel Science Foundation
Award: G8153456840
OpenAlex ID: W7221820815