PreprintCC BY 4.0arXiv
There are no unconditional Schauder frames of exponentials in Lp spaces, p ≠ 2
Abstract
We proved recently that there are no unconditional Schauder frames of exponentials in the space Lp(Ω), 1 ≤ p < 2, for any set Ω⊂ ℝd 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 Lp(Ω), p ≠ 2, without any additional assumptions on the set Ω of finite measure other than measurability.
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BibTeX
@misc{lev2026there,
title = {{There are no unconditional Schauder frames of exponentials in $L^p$ spaces, $p \ne 2$}},
author = {Nir Lev and Anton Tselishchev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14842},
eprint = {2610.14842},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14842},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - There are no unconditional Schauder frames of exponentials in L^p spaces, p ≠ 2
AU - Nir Lev
AU - Anton Tselishchev
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14842
UR - https://arxiv.org/abs/2610.14842
AB - We proved recently that there are no unconditional Schauder frames of exponentials in the space L^p(Ω), 1 ≤ p < 2, for any set Ω⊂ 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 ≠ 2, without any additional assumptions on the set Ω of finite measure other than measurability.
ER -