2025/12/5
Mohammad Reza Azimi

Mohammad Reza Azimi

Academic rank: Associate Professor
ORCID:
Education: PhD.
H-Index:
Faculty: Faculty of Basic Sciences
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E-mail: mhreza.azimi [at] gmail.com
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Research

Title
Dynamics of weighted composition operators on Stein manifolds
Type
JournalPaper
Keywords
holomorphic functions, weighted composition, hypercyclic, convexity, Stein manifold
Year
2025
Journal Analele Stiintifice ale Universitatii Al I Cuza din Iasi-Serie Noua-Matematica
DOI
Researchers Firooz Pashaie ، Mohammad Reza Azimi ، Mohammad Shahidi

Abstract

In the present paper, we investigate the hypercyclicity of weighted composition operators acting on the space of holomorphic functions on a connected finite-dimensional Stein manifold. Let \psi be a holomorphic self-map on a connected Stein n-manifold \Omega and \omega\in {H}(\Omega) a holomorphic function. We study the hypercyclicity of weighted composition operator \Pi_{\psi, \omega}: {H}(\Omega)\to {H}(\Omega) defined by \Pi_{\psi, \omega}(f):= \omega\ ...(f\circ \psi) for every f\in {H}(\Omega). We prove that \Pi_{\psi, \omega} is hypercyclic if and only if \omega(p) \neq 0 at each p \in \Omega , \psi is univalent without fixed points in \Omega, \psi(\Omega) is a Runge domain and for every compact holomorphically convex set K\subset \Omega there is an integer n such that K \cap \psi^{[n]}(K) = \emptyset and their union is holomorphically convex.