2-complex symmetric weighted composition operators on Fock space

The aim of the present paper is to completely characterize 2-complex symmetric weighted composition operators $ W_{e^{\overline{p}z, az+b}} $ with the conjugations $ C $ and $ C_{r, s, t} $ defined by $ Cf(z) = \overline{f(\bar{z})} $ and $ C_{r, s, t}f(z) = te^{sz}\overline{f(\overline{rz+s})} $ on...

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Published inAIMS mathematics Vol. 8; no. 9; pp. 21781 - 21792
Main Authors Bai, Hong-bin, Jiang, Zhi-jie, Hu, Xiao-bo, Li, Zuo-an
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
2-complex symmetric operator
fock space
reproducing kernel function
weighted composition operator
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Summary:The aim of the present paper is to completely characterize 2-complex symmetric weighted composition operators $ W_{e^{\overline{p}z, az+b}} $ with the conjugations $ C $ and $ C_{r, s, t} $ defined by $ Cf(z) = \overline{f(\bar{z})} $ and $ C_{r, s, t}f(z) = te^{sz}\overline{f(\overline{rz+s})} $ on Fock space by building the relations between the parameters $ a $, $ b $, $ p $, $ r $, $ s $ and $ t $. Some examples of such operators are also given.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20231111