Stević-Sharma type operators on Fock spaces in several variables
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 1241-1263
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Let $\varphi $ be an entire self-map of $\mathbb {C}^N$, $u_0$ be an entire function on $\mathbb {C}^N$ and ${\bf u}=(u_1,\cdots ,u_N)$ be a vector-valued entire function on $\mathbb {C}^N$. We extend the Stević-Sharma type operator to the classcial Fock spaces, by defining an operator $T_{u_0,{\bf u},\varphi }$ as follows: $$\openup -.4pt T_{u_0,{\bf u},\varphi }f=u_0\cdot f\circ \varphi +\sum _{i=1}^Nu_i\cdot \frac {\partial f}{\partial z_i}\circ \varphi . $$ We investigate the boundedness and compactness of $T_{u_0,{\bf u},\varphi }$ on Fock spaces. The complex symmetry and self-adjointness of $T_{u_0,{\bf u},\varphi }$ are also characterized.
Let $\varphi $ be an entire self-map of $\mathbb {C}^N$, $u_0$ be an entire function on $\mathbb {C}^N$ and ${\bf u}=(u_1,\cdots ,u_N)$ be a vector-valued entire function on $\mathbb {C}^N$. We extend the Stević-Sharma type operator to the classcial Fock spaces, by defining an operator $T_{u_0,{\bf u},\varphi }$ as follows: $$\openup -.4pt T_{u_0,{\bf u},\varphi }f=u_0\cdot f\circ \varphi +\sum _{i=1}^Nu_i\cdot \frac {\partial f}{\partial z_i}\circ \varphi . $$ We investigate the boundedness and compactness of $T_{u_0,{\bf u},\varphi }$ on Fock spaces. The complex symmetry and self-adjointness of $T_{u_0,{\bf u},\varphi }$ are also characterized.
Classification :
30H20, 46E15, 47B33
Keywords: Stević-Sharma operator; Fock space; $\mathcal {J}$-symmetry
Keywords: Stević-Sharma operator; Fock space; $\mathcal {J}$-symmetry
@article{10_21136_CMJ_2024_0244_24,
author = {Ma, Lijun and Yang, Zicong},
title = {Stevi\'c-Sharma type operators on {Fock} spaces in several variables},
journal = {Czechoslovak Mathematical Journal},
pages = {1241--1263},
year = {2024},
volume = {74},
number = {4},
doi = {10.21136/CMJ.2024.0244-24},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2024.0244-24/}
}
TY - JOUR AU - Ma, Lijun AU - Yang, Zicong TI - Stević-Sharma type operators on Fock spaces in several variables JO - Czechoslovak Mathematical Journal PY - 2024 SP - 1241 EP - 1263 VL - 74 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2024.0244-24/ DO - 10.21136/CMJ.2024.0244-24 LA - en ID - 10_21136_CMJ_2024_0244_24 ER -
%0 Journal Article %A Ma, Lijun %A Yang, Zicong %T Stević-Sharma type operators on Fock spaces in several variables %J Czechoslovak Mathematical Journal %D 2024 %P 1241-1263 %V 74 %N 4 %U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2024.0244-24/ %R 10.21136/CMJ.2024.0244-24 %G en %F 10_21136_CMJ_2024_0244_24
Ma, Lijun; Yang, Zicong. Stević-Sharma type operators on Fock spaces in several variables. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 1241-1263. doi: 10.21136/CMJ.2024.0244-24
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