Stević-Sharma type operators on Fock spaces in several variables

Lijun Ma; Zicong Yang

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 4, page 1241-1263
  • ISSN: 0011-4642

Abstract

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Let ϕ be an entire self-map of ℂ N , u 0 be an entire function on ℂ N and 𝐮 = ( u 1 , ⋯ , u N ) be a vector-valued entire function on ℂ N . We extend the Stević-Sharma type operator to the classcial Fock spaces, by defining an operator T u 0 , 𝐮 , ϕ as follows: - . 4 p t T u 0 , 𝐮 , ϕ f = u 0 · f ∘ ϕ + ∑ i = 1 N u i · ∂ f ∂ z i ∘ ϕ . We investigate the boundedness and compactness of T u 0 , 𝐮 , ϕ on Fock spaces. The complex symmetry and self-adjointness of T u 0 , 𝐮 , ϕ are also characterized.

How to cite

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Ma, Lijun, and Yang, Zicong. "Stević-Sharma type operators on Fock spaces in several variables." Czechoslovak Mathematical Journal 74.4 (2024): 1241-1263. <http://eudml.org/doc/299656>.

@article{Ma2024,
abstract = {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: \[-.4pt T\_\{u\_0,\{\bf u\},\varphi \}f=u\_0\cdot f\circ \varphi +\sum \_\{i=1\}^Nu\_i\cdot \frac\{\partial f\}\{\partial z\_i\}\circ \varphi . \] 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.},
author = {Ma, Lijun, Yang, Zicong},
journal = {Czechoslovak Mathematical Journal},
keywords = {Stević-Sharma operator; Fock space; $\mathcal \{J\}$-symmetry},
language = {eng},
number = {4},
pages = {1241-1263},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stević-Sharma type operators on Fock spaces in several variables},
url = {http://eudml.org/doc/299656},
volume = {74},
year = {2024},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 4
SP - 1241
EP - 1263
AB - 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: \[-.4pt T_{u_0,{\bf u},\varphi }f=u_0\cdot f\circ \varphi +\sum _{i=1}^Nu_i\cdot \frac{\partial f}{\partial z_i}\circ \varphi . \] 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.
LA - eng
KW - Stević-Sharma operator; Fock space; $\mathcal {J}$-symmetry
UR - http://eudml.org/doc/299656
ER -

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