We study composition-differentiation operators acting on the Bergman and Dirichlet space of the open unit disk. We first characterize the compactness of composition-differentiation operator on weighted Bergman spaces. We shall then prove that for an analytic self-map $\varphi$ on the open unit disk $\mathbb{D}$, the induced composition-differentiation operator is bounded with dense range if and only if $\varphi$ is univalent and the polynomials are dense in the Bergman space on $\Omega:=\varphi(\mathbb{D})$.
composition-differentiation operator Bergman space Dirichlet space compact operator dense-range operator
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Erken Görünüm Tarihi | 15 Ağustos 2023 |
Yayımlanma Tarihi | 27 Haziran 2024 |
Yayımlandığı Sayı | Yıl 2024 Cilt: 53 Sayı: 3 |