2-complex symmetric weighted composition operators on Fock space

Hong-bin Bai; Zhi-jie Jiang; Xiao-bo Hu; Zuo-an Li; Hong-bin Bai; Zhi-jie Jiang; Xiao-bo Hu; Zuo-an Li

doi:10.3934/math.20231111

AIMS Mathematics

2023, Volume 8, Issue 9: 21781-21792. doi: 10.3934/math.20231111

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Research article

2-complex symmetric weighted composition operators on Fock space

1.
School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, China
2.
South Sichuan Center for Applied Mathematics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, China
3.
Department of Normal Education, Meishan Vocational and Technical College, Meishan, Sichuan, 620010, China

Received: 23 April 2023 Revised: 19 June 2023 Accepted: 29 June 2023 Published: 10 July 2023
MSC : 30H10, 47B38

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.
- Fock space,
- weighted composition operator,
- 2-complex symmetric operator,
- reproducing kernel function
Citation: Hong-bin Bai, Zhi-jie Jiang, Xiao-bo Hu, Zuo-an Li. 2-complex symmetric weighted composition operators on Fock space[J]. AIMS Mathematics, 2023, 8(9): 21781-21792. doi: 10.3934/math.20231111

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Abstract

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.

References

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