On the equivalence of the Euler-Pommier operators in spaces of analytic functions

• Date: 1996
• Main Authors: Nagnibida, N. I., Нагнибіда, Н. І.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1996
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5269
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

In the space A (θ) of all one-valued functions f(z) analytic in an arbitrary region G ⊂ ℂ (0 ∈ G) with the topology of compact convergence, we establish necessary and sufficient conditions for the equivalence of the operators L 1=α n z n Δ n + ... + α1 zΔ+α0 E and L 2= z n a n (z)Δ n + ... +...