Open AccessSTABILITY OF THE DEFECTS OF A FIRST-ORDER ENTIRE CURVE
Author(s) -
I. Ye. Ovchar,
Ya. I. Savchuk
Publication year - 2018
Publication title -
prikarpatsʹkij vìsnik ntš. čislo
Language(s) - English
Resource type - Journals
ISSN - 2304-7399
DOI - 10.31471/2304-7399-2018-2(46)-17-20
Subject(s) - argument (complex analysis) , transformation (genetics) , mathematics , meromorphic function , linear map , order (exchange) , function (biology) , pure mathematics , economics , biochemistry , chemistry , finance , evolutionary biology , biology , gene
When linearly transforming the argument of a whole curve, it is naturally to expect the invariability of the main characteristics of the curve, particularly its defects. The questions of the change of defects of meromorphic functions with linear transformation of the argument were taken by Dyugo, Goldberg and others. The unexpected, at first glance, results of a change in the defects of a meromorphic function under linear transformation of the argument, are obtained. The authors of this article have previously constructed a whole curve of infinite order, for which the magnitude of the defect of a given vector under the linear transformation of the argument is being changed. In this paper, the first order whole curve is constructed, such that, on the one hand, a certain vector will not be Nevanlinna’s defective , while on the other hand, it is defective under the linear transformation of the argument.