Details
| Original language | English |
|---|---|
| Article number | 111265 |
| Journal | Journal of functional analysis |
| Volume | 290 |
| Issue number | 4 |
| Early online date | 4 Nov 2025 |
| Publication status | Published - 15 Feb 2026 |
Abstract
We investigate Wiener's Tauberian theorem from the perspective of limit functions, which results in several new versions of the Tauberian theorem. Based on this, we formulate and prove analogous Tauberian theorems for operators in the sense of quantum harmonic analysis. Using these results, we characterize the class of slowly oscillating operators and show that this class is strictly larger than the class of uniformly continuous operators. Finally, we discuss uniform versions of Wiener's Tauberian theorem and its operator analogue and provide an application of this in operator theory.
Keywords
- Quantum harmonic analysis, Wiener Tauberian theorem
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
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In: Journal of functional analysis, Vol. 290, No. 4, 111265, 15.02.2026.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Wiener's Tauberian theorem in classical and quantum harmonic analysis
AU - Fulsche, Robert
AU - Luef, Franz
AU - Werner, Reinhard F.
N1 - Publisher Copyright: © 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license. http://creativecommons.org/licenses/by/4.0/
PY - 2026/2/15
Y1 - 2026/2/15
N2 - We investigate Wiener's Tauberian theorem from the perspective of limit functions, which results in several new versions of the Tauberian theorem. Based on this, we formulate and prove analogous Tauberian theorems for operators in the sense of quantum harmonic analysis. Using these results, we characterize the class of slowly oscillating operators and show that this class is strictly larger than the class of uniformly continuous operators. Finally, we discuss uniform versions of Wiener's Tauberian theorem and its operator analogue and provide an application of this in operator theory.
AB - We investigate Wiener's Tauberian theorem from the perspective of limit functions, which results in several new versions of the Tauberian theorem. Based on this, we formulate and prove analogous Tauberian theorems for operators in the sense of quantum harmonic analysis. Using these results, we characterize the class of slowly oscillating operators and show that this class is strictly larger than the class of uniformly continuous operators. Finally, we discuss uniform versions of Wiener's Tauberian theorem and its operator analogue and provide an application of this in operator theory.
KW - Quantum harmonic analysis
KW - Wiener Tauberian theorem
UR - http://www.scopus.com/inward/record.url?scp=105023851765&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2025.111265
DO - 10.1016/j.jfa.2025.111265
M3 - Article
AN - SCOPUS:105023851765
VL - 290
JO - Journal of functional analysis
JF - Journal of functional analysis
SN - 0022-1236
IS - 4
M1 - 111265
ER -