| Title:
|
On the powers of quasihomogeneous Toeplitz operators (English) |
| Author:
|
Bouhali, Aissa |
| Author:
|
Bendaoud, Zohra |
| Author:
|
Louhichi, Issam |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
4 |
| Year:
|
2021 |
| Pages:
|
1049-1061 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present sufficient conditions for the existence of $p$th powers of a quasihomogeneous Toeplitz operator $T_{{\rm e}^{{\rm i} s\theta }\psi }$, where $\psi $ is a radial polynomial function and $p$, $s$ are natural numbers. A large class of examples is provided to illustrate our results. To our best knowledge those examples are not covered by the current literature. The main tools in the proof of our results are the Mellin transform and some classical theorems of complex analysis. (English) |
| Keyword:
|
quasihomogeneous Toeplitz operator |
| Keyword:
|
Mellin transform |
| MSC:
|
30-00 |
| MSC:
|
30H20 |
| MSC:
|
44A99 |
| MSC:
|
47B35 |
| idZBL:
|
Zbl 07442473 |
| idMR:
|
MR4339110 |
| DOI:
|
10.21136/CMJ.2021.0193-20 |
| . |
| Date available:
|
2021-11-08T16:00:23Z |
| Last updated:
|
2024-01-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149237 |
| . |
| Reference:
|
[1] Ahern, P., Čučković, Ž.: A theorem of Brown-Halmos type for Bergman space Toeplitz operators.J. Funct. Anal. 187 (2001), 200-210. Zbl 0996.47037, MR 1867348, 10.1006/jfan.2001.3811 |
| Reference:
|
[2] Cohen, A. M.: Numerical Methods for Laplace Transform Inversion.Numerical Methods and Algorithms 5. Springer, New York (2007). Zbl 1127.65094, MR 2325479, 10.1007/978-0-387-68855-8 |
| Reference:
|
[3] Čučković, Ž., Rao, N. V.: Mellin transform, monomial symbols, and commuting Toeplitz operators.J. Funct. Anal. 154 (1998), 195-214. Zbl 0936.47015, MR 1616532, 10.1006/jfan.1997.3204 |
| Reference:
|
[4] Godement, R.: Analysis III. Analytic and Differential Functions, Manifolds and Riemann Surfaces.Universitext. Springer, Cham (2015). Zbl 1318.30001, MR 3328588, 10.1007/978-3-319-16053-5 |
| Reference:
|
[5] Louhichi, I.: Powers and roots of Toeplitz operators.Proc. Am. Math. Soc. 135 (2007), 1465-1475. Zbl 1112.47023, MR 2276656, 10.1090/S0002-9939-06-08626-6 |
| Reference:
|
[6] Louhichi, I., Rao, N. V.: Roots of Toeplitz operators on the Bergman space.Pac. J. Math. 252 (2011), 127-144. Zbl 1237.47033, MR 2862145, 10.2140/pjm.2011.252.127 |
| Reference:
|
[7] Louhichi, I., Rao, N. V., Yousef, A.: Two questions on products of Toeplitz operators on the Bergman space.Complex Anal. Oper. Theory 3 (2009), 881-889. Zbl 1195.47018, MR 2570117, 10.1007/s11785-008-0097-3 |
| Reference:
|
[8] Louhichi, I., Strouse, E., Zakariasy, L.: Products of Toeplitz operators on the Bergman space.Integral Equations Oper. Theory 54 (2006), 525-539. Zbl 1109.47023, MR 2222982, 10.1007/s00020-005-1369-1 |
| Reference:
|
[9] Louhichi, I., Zakariasy, L.: On Toeplitz operators with quasihomogeneous symbols.Arch. Math. 85 (2005), 248-257. Zbl 1088.47019, MR 2172383, 10.1007/s00013-005-1198-0 |
| Reference:
|
[10] Remmert, R.: Classical Topics in Complex Function Theory.Graduate Texts in Mathematics 172. Springer, New York (1998). Zbl 0895.30001, MR 1483074, 10.1007/978-1-4757-2956-6 |
| . |
