RUS  ENG
Full version
JOURNALS // Ufimskii Matematicheskii Zhurnal // Archive

Ufimsk. Mat. Zh., 2025 Volume 17, Issue 1, Pages 62–76 (Mi ufa721)

Interpolation sequences in area Privalov classes in disk

E. G. Rodikova

Bryansk State University, Bezhitskaya str. 14, 241050, Bryansk, Russia

Abstract: In the work we obtain a necessary and sufficient condition for the zeros of analytic functions in area Privalov classes $\tilde{\Pi}_q$ $(0<q<1)$ in the unit circle $D=\{z\in \mathbb{C}: |z|<1\}$ located in the Stolz angles. We solve the free interpolation problem in these classes under the condition that the interpolation nodes are located in the Stolz angles. We also solve the interpolation problem in the area Privalov classes in circle on Carleson sets.

Keywords: analytic function, zeros, interpolation, area Privalov class, Stolz angle, unit circle.

UDC: 517.53

MSC: 30E05, 30H15, 30H50

Received: 08.05.2024


 English version:
Ufa Mathematical Journal, 2025, 17:1, 59–73


© Steklov Math. Inst. of RAS, 2025