g-Loewner Chains and the Graham–Kohr Extension Operator in Complex Banach Spaces
Year: 2025
Type: article
Abstract: In this paper we focus our attention on the Graham–Kohr extension operator $$\Psi _{\alpha }$$ Ψ α (introduced by Graham and Kohr in Complex Var. Theory Appl. 47:59–72, 2002) defined by $$\begin{aligned} \Psi _{\alpha }(f)(z_1,w)=\bigg (f(z_1),\bigg (\dfrac{f(z_1)}{z_1}\bigg )^{\alpha }w \bigg ), \quad (z_1,w)\in \Omega _{p,r}, \, \alpha \in [0,1] \end{aligned}$$ Ψ α ( f ) ( z 1 , w ) = ( f ( z 1 ) , ( f ( z 1 ) z 1 ) α w ) , ( z 1 , w ) ∈ Ω p , r , α ∈ [ 0 , 1 ] and its properties on the domain $$\Omega _{p,r}=\{(z_1,w)\in \mathbb {C}\times X:\vert z_1\vert ^p+\Vert w\Vert ^r_X<1\}$$ Ω p , r = { ( z 1 , w ) ∈ C × X : | z 1 | p + ‖ w ‖ X r < 1 } , where X is a co
Author: Eduard Ştefan Grigoriciuc
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4408987236