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Keywords:
Stević-Sharma operator; Fock space; $\mathcal {J}$-symmetry
Stević-Sharma operator; Fock space; $\mathcal {J}$-symmetry
Summary:
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.
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