Bewaard in:
| Hoofdauteur: | |
|---|---|
| Formaat: | Preprint |
| Gepubliceerd in: |
2020
|
| Onderwerpen: | |
| Online toegang: | https://arxiv.org/abs/2002.07288 |
| Tags: |
Voeg label toe
Geen labels, Wees de eerste die dit record labelt!
|
Inhoudsopgave:
- In this article, we study the complex symmetry of compositions operators $C_ϕf=f\circ ϕ$ induced on weighted Bergman spaces $A^2_β(\mathbb{D}),\ β\geq -1,$ by analytic self-maps of the unit disk. One of ours main results shows that $ϕ$ has a fixed point in $\mathbb{D}$ whenever $C_ϕ$ is complex symmetric. Our works establishes a strong relation between complex symmetry and cyclicity. By assuming $β\in \mathbb{N}$ and $ϕ$ is an elliptic automorphism of $\mathbb{D}$ which not a rotation, we show that $C_ϕ$ is not complex symmetric whenever $ϕ$ has order greater than $2(3+β).$