Concentration index of a subharmonic function of zeroth order

Гольдберг, А. А.; Zabolotskii, N. V.

doi:10.1007/bf01141775

Cited by 9 publications

(6 citation statements)

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“…moreover, the estimates (3) and (4) Proof. Suppose that /f and e, 0 <//< 1, 0 < ~ < 1, are arbitrary numbers.…”

mentioning

confidence: 99%

Strongly regular growth of entire functions of order zero

Zabolotskii¹

1998

Math Notes

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ABSTRACT. For entire functions of order zero we introduce a new concept of regularity of growth, which is shown to possess properties similar to those which characterize the concept of totally regular growth of entire functions of finite order in the sense of Levin-Pfliiger.KEY WORDS: entire function of order zero, regularity of growth, function of totally regular growth, function of strongly regular growth. Let n(r, a, fl) be the number of roots of the function f in the sector {z : Izl <_ r, a < argz <_ fl}. We say [1, pp. 118-119] that the set of roots of an entire function has angular density if the limitexists for all a, 1~ with the exception, perhaps, of ~ or fl belonging to some countable set. In this case, for a given a, the relation A(fl) -A(a) = A(a, fl) defines a nondecreasing function A(fl) up to an arbitrary constant. In [1, Chaps. 2 and 3] a complete description of entire functions of totally regular growth is given. In particular, if p is noninteger, then the entire function f is a function of totally regular growth if and only if the set of its roots has angular density; moreover,

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“…moreover, the estimates (3) and (4) Proof. Suppose that /f and e, 0 <//< 1, 0 < ~ < 1, are arbitrary numbers.…”

mentioning

confidence: 99%

Strongly regular growth of entire functions of order zero

Zabolotskii¹

1998

Math Notes

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“…From the results of [6] it follows that if we similarly introduce the notion of c.r.g. for the class H 0 of zero-order entire functions, then the obtained theory becomes ineffective.…”

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confidence: 99%

Binomial asymptotics for the logarithmic derivative of zero-order entire functions with zeros along curves of regular rotation

Zabolots’kyi¹,

Basiuk²,

Mostova³

2019

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“…Пусть ρ(r) -н. у. п., удовлетворяющий условию (4). Пусть a n -такая допустимая последовательность, что выполняется неравенство (8).…”

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An interpolation problem in the class of entire functions of zero order

Bozhenko¹,

Grishin²,

Малютин³

et al. 2015

Известия Российской академии наук. Серия математическая

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Интерполяционная задача в классе целых функций нулевого порядка Получены два критерия разрешимости задачи простой свободной интерполяции в классе целых функций заранее не фиксированного конечного типа относительно нулевого уточненного порядка ρ(r), на который налагается только естественное ограничение, связанное с отличием рассматриваемого класса от множества полиномов. Один из критериев сформулирован в терминах меры, порожденной узлами интерполяции, другойв терминах канонического произведения, порожденного этими узлами. Библиография: 9 наименований. Ключевые слова: нулевой уточненный порядок, свободная интерполяция, интерполяционная последовательность, каноническое произведение, мера Дирака, неванлинновская считающая функция.

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Concentration index of a subharmonic function of zeroth order

Cited by 9 publications

References 1 publication

Strongly regular growth of entire functions of order zero

Strongly regular growth of entire functions of order zero

Binomial asymptotics for the logarithmic derivative of zero-order entire functions with zeros along curves of regular rotation

An interpolation problem in the class of entire functions of zero order

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