STABILITY OF THE DEFECTS OF A FIRST-ORDER ENTIRE CURVE
DOI:
https://doi.org/10.31471/2304-7399-2018-2(46)-17-20Keywords:
meromophic function, whole curve, growth’s characteris- ric, approximation function, Nevanlinna’s defective vector, magnitude of a defect.Abstract
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.
References
Петренко В.П. Целые кривые. Ч.: Вища школа, – 1984. – 136 с.
Овчар І.Є., Савчук Я.І. Стійкість дефектів цілої кривої скінченного порядку // Прикарпатський вісник НТШ. Число. – 2018. – No1(45). – с. 17-20.
Гольдберг А.А., Островский И.В. Распределение значений мероморфных функций. – М.: Наука, 1970. – 592 с.
Левин Б.Я. Распределение корней целых функций. – М., ГИТТЛ, 1956. – 632 с.
