Weighted composition operators on the class of subordinate functions

Perumal Muthukumar; Saminathan Ponnusamy

Weighted composition operators on the class of subordinate functions

Functional Analysis 2018-02-07 v1

Authors: Perumal Muthukumar , Saminathan Ponnusamy

Abstract

In this article, we study the weighted composition operators preserving the class $\mathcal{P}_{\alpha}$ of analytic functions subordinate to $\frac{1+\alpha z}{1-z}$ for $|\alpha|\leq 1, \alpha \neq -1$ . Some of its consequences and examples for some special cases are presented. Furthermore, we discuss about the fixed points of weighted composition operators.

Keywords

composition operators operator theory weighted inequalities

Cite

@article{arxiv.1802.01828,
  title  = {Weighted composition operators on the class of subordinate functions},
  author = {Perumal Muthukumar and Saminathan Ponnusamy},
  journal= {arXiv preprint arXiv:1802.01828},
  year   = {2018}
}

Comments

11 pages; To appear in Rocky Mountain Journal of Mathematics (exclusion of the results of Section 6)

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