| Title:
|
On products of some Toeplitz operators on polyanalytic Fock spaces (English) |
| Author:
|
Casseli, Irène |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
369-379 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The purpose of this paper is to study the Sarason's problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols $f$ and $g$, we establish a necessary and sufficient condition for the boundedness of some Toeplitz products $ T_{f}T_{\bar g}$ subjected to certain restriction on $f$ and $g$. We also characterize this property in terms of the Berezin transform. (English) |
| Keyword:
|
polyanalytic function |
| Keyword:
|
Toeplitz operator |
| Keyword:
|
Fock space |
| Keyword:
|
Sarason's problem |
| MSC:
|
30G30 |
| MSC:
|
30H20 |
| MSC:
|
46E22 |
| MSC:
|
47B35 |
| idZBL:
|
07217140 |
| idMR:
|
MR4111848 |
| DOI:
|
10.21136/CMJ.2019.0334-18 |
| . |
| Date available:
|
2020-06-17T12:31:50Z |
| Last updated:
|
2022-07-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148234 |
| . |
| Reference:
|
[1] Abreu, L. D.: On the structure of Gabor and super Gabor spaces.Monatsh. Math. 161 (2010), 237-253. Zbl 1206.46029, MR 2726212, 10.1007/s00605-009-0177-0 |
| Reference:
|
[2] Aleman, A., Pott, S., Reguera, M. C.: Sarason conjecture on the Bergman space.Int. Math. Res. Not. 2017 (2017), 4320-4349. Zbl 1405.30055, MR 3674172, 10.1093/imrn/rnw134 |
| Reference:
|
[3] Askour, N., Intissar, A., Mouayn, Z.: Espaces de Bargmann généralisés et formules explicites pour leurs noyaux reproduisants.C. R. Acad. Sci., Paris, Sér. I, Math. 325 (1997), 707-712 French. Zbl 0892.32018, MR 1483703, 10.1016/S0764-4442(97)80045-6 |
| Reference:
|
[4] Balk, M. B.: Polyanalytic Functions.Mathematical Research 63. Akademie Verlag, Berlin (1991). Zbl 0764.30038, MR 1184141 |
| Reference:
|
[5] Bommier-Hato, H., Youssfi, E. H., Zhu, K.: Sarason's Toeplitz product problem for a class of Fock spaces.Bull. Sci. Math. 141 (2017), 408-442. Zbl 1377.47010, MR 3667593, 10.1016/j.bulsci.2017.03.002 |
| Reference:
|
[6] Cho, H. R., Park, J.-D., Zhu, K.: Products of Toeplitz operators on the Fock space.Proc. Am. Math. Soc. 142 (2014), 2483-2489. Zbl 1303.47035, MR 3195769, 10.1090/S0002-9939-2014-12110-1 |
| Reference:
|
[7] Haimi, A., Hedenmalm, H.: The polyanalytic Ginibre ensembles.J. Stat. Phys. 153 (2013), 10-47. Zbl 1278.82068, MR 3100813, 10.1007/s10955-013-0813-x |
| Reference:
|
[8] Nazarov, F.: A counterexample to Sarason's conjecture.Available at http://users.math.msu.edu/users/fedja/prepr.html. |
| Reference:
|
[9] Sarason, D.: Exposed points in $H^1$. I.The Gohberg Anniversary Collection, Vol. II Operator Theory: Advances and Applications 41. Birkhäuser, Basel (1989), 485-496. Zbl 0678.46019, MR 1038352 |
| Reference:
|
[10] Sarason, D.: Products of Toeplitz operators.Linear and Complex Analysis. Problem Book 3, Part I V. P. Havin, N. K. Nikolskii Lecture Notes in Mathematics 1573. Springer, Berlin (1994), 318-319. Zbl 0893.30036, MR 1334345, 10.1007/BFb0100208 |
| . |
