Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 3017-3060 |
| Seitenumfang | 44 |
| Fachzeitschrift | Journal of functional analysis |
| Jahrgang | 268 |
| Ausgabenummer | 10 |
| Publikationsstatus | Veröffentlicht - 15 Mai 2015 |
Abstract
In the setting of the Bergman space over the disk or the ball, it has been known that two Toeplitz operators with bounded pluriharmonic symbols can (semi-)commute only in the trivial cases. In this paper we study the analogues on the Fock space over the multi-dimensional complex space. As is the case in various other settings, we are naturally led to the problem of characterizing a certain type of fixed points of the Berezin transform. For such fixed points, we obtain a complete characterization by means of eigenfunctions of the Laplacian. We also obtain other characterizations. In particular, it turns out that there are many nontrivial cases on the Fock space for (semi-)commuting Toeplitz operators with pluriharmonic symbols. All in all our results reveal that the situation on the Fock space appears to be much more complicated than that on the classical Bergman space setting, which partly is caused by the unboundedness of the operator symbols. Some of our results are restricted to the one-variable case and the corresponding several-variable case is left open.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
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in: Journal of functional analysis, Jahrgang 268, Nr. 10, 15.05.2015, S. 3017-3060.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Commuting Toeplitz operators with pluriharmonic symbols on the Fock space
AU - Bauer, Wolfram
AU - Choe, Boo Rim
AU - Koo, Hyungwoon
N1 - Publisher Copyright: © 2015 Elsevier Inc. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2015/5/15
Y1 - 2015/5/15
N2 - In the setting of the Bergman space over the disk or the ball, it has been known that two Toeplitz operators with bounded pluriharmonic symbols can (semi-)commute only in the trivial cases. In this paper we study the analogues on the Fock space over the multi-dimensional complex space. As is the case in various other settings, we are naturally led to the problem of characterizing a certain type of fixed points of the Berezin transform. For such fixed points, we obtain a complete characterization by means of eigenfunctions of the Laplacian. We also obtain other characterizations. In particular, it turns out that there are many nontrivial cases on the Fock space for (semi-)commuting Toeplitz operators with pluriharmonic symbols. All in all our results reveal that the situation on the Fock space appears to be much more complicated than that on the classical Bergman space setting, which partly is caused by the unboundedness of the operator symbols. Some of our results are restricted to the one-variable case and the corresponding several-variable case is left open.
AB - In the setting of the Bergman space over the disk or the ball, it has been known that two Toeplitz operators with bounded pluriharmonic symbols can (semi-)commute only in the trivial cases. In this paper we study the analogues on the Fock space over the multi-dimensional complex space. As is the case in various other settings, we are naturally led to the problem of characterizing a certain type of fixed points of the Berezin transform. For such fixed points, we obtain a complete characterization by means of eigenfunctions of the Laplacian. We also obtain other characterizations. In particular, it turns out that there are many nontrivial cases on the Fock space for (semi-)commuting Toeplitz operators with pluriharmonic symbols. All in all our results reveal that the situation on the Fock space appears to be much more complicated than that on the classical Bergman space setting, which partly is caused by the unboundedness of the operator symbols. Some of our results are restricted to the one-variable case and the corresponding several-variable case is left open.
KW - Berezin transform
KW - Commuting Toeplitz operators
KW - Fock space
KW - Primary
KW - Secondary
UR - http://www.scopus.com/inward/record.url?scp=84926421304&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2015.03.003
DO - 10.1016/j.jfa.2015.03.003
M3 - Article
AN - SCOPUS:84926421304
VL - 268
SP - 3017
EP - 3060
JO - Journal of functional analysis
JF - Journal of functional analysis
SN - 0022-1236
IS - 10
ER -