Slice regular Besov spaces of hyperholomorphic functions and composition operators

Kumar, Sanjay; Manzoor, Khalid

doi:10.48550/arxiv.1609.02394

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Weighted Composition Operators1

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2019

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“…By the representation formula (Proposition 2.4), we get the extension C ϕ h to the whole H. The systematical research of composition operators on holomorphic functions in one complex variables is a fairly active field, see the two books [4] by Cowen and Mac-Cluer, and [15] by Shapiro. As regards to recent topic about composition operators on slice regular spaces of hyperholomorphic functions, we refer to [12,16] and their references therein.…”

Section: Weighted Composition Operatorsmentioning

confidence: 99%

A Left Linear Weighted Composition Operator on Quaternionic Fock Space

Liang

2019

Results Math

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In this paper, we study the weighted composition operator on the Fock space F 2 (H) of slice regular functions. First, we characterize the boundedness and compactness of the weighted composition operator. Subsequently, we describe all the isometric composition operators. Finally, we introduce a kind of (right)-anticomplex-linear weighted composition operator on F 2 (H) and obtain some concrete forms such that this (right)-anti-linear weighted composition operator is a (right)-conjugation. Specially, we present equivalent conditions ensuring weighted composition operators which are conjugate C a,b,c −commuting or complex C a,b,c − symmetric on F 2 (H), which generalized the classical results on F 2 (C). At last part of the paper, we exhibit the closed expression for the kernel function of F 2 (H).2010 Mathematics Subject Classification. Primary: 30G35, 47B38, 47B15, 30H20.

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Section: Weighted Composition Operatorsmentioning

confidence: 99%