WEAKLY REGULAR SETS IN THE SPACE OF FUNCTIONS OF FINITE ORDER IN THE HALF-PLANE

Author(s):  A.L. Gusev, Kursk State University, Kursk , Russia, cmex1990goose@yandex.ru

Issue:  Volume 51, № 2

Rubric:  Mathematics

Annotation:  In this article, the concept of a weakly regular set in the space of analytical functions of the finite order greater than unity in the upper half-plane of complex variable is introduced. The sequence , C+, is called weakly regular in C+ by order if one of the following conditions or is satisfied: 1) Among the points of the set A there are no multiples; 2) for any there exists such that for the disks of radius with centers do not intersect; 3) for any . 1’) Among the points of the set A there are no multiples and there are no points with the same modules; 2’) conditions 1) and 3) are true; 3’) for any there exists such that for the inequality are true. It is proved that such sets are interpolation in the sense of free interpolation in this space.

Keywords:  upper half-plane, finite order, weakly regular set, free interpolation

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