Generalization of the Lindelöf Theorem to the Case of Boutroux Proximate Order. II

Malyutin, K. G.; Кабанко, М. В.; Kostenko, I. V.

doi:10.1007/s10958-022-06020-6

Cited by 3 publications

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References 3 publications

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“…In this paper, we extend the results of [3] to subharmonic functions on the complex plane and the half-plane. Note that the difference between the Boutroux order and the Valiron order is that the lower order may not be equal to the upper one.…”

Section: Let Us Denotementioning

confidence: 70%

“…In [1], Theorems 2 and 3 are extended to entire functions whose growth is determined by the Valiron proximate order (see [1,Chapter I,Theorems 17 and 18]). In the paper of authors [3], Theorems 2 and 3 are extended to entire functions whose growth is determined by the Boutroux proximate order [4]. The coefficient characterization of the growth of entire and meromorphic functions is important in many questions of analysis.…”

Section: Let Us Denotementioning

confidence: 99%

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On the Type of Subharmonic Functions of Finite Order

Malyutin

Кабанко

2022

J Math Sci

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Theorems establishing a connection between the type of an entire function and the distribution of its zeros play an important role in the theory of entire functions. The classical Lindelöf theorem asserts that zeros of an entire function of finite integer order and normal type possess a certain symmetry property. We prove counterparts of the Lindelöf theorem in the spaces of subharmonic functions in the complex plane and in the half-plane the growth of which is determined by the proximate order in the sense of Boutroux. The results are formulated in the terms of the upper density and the upper balance of the Riesz measure and the full measure of functions.

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Section: Let Us Denotementioning

confidence: 70%

Section: Let Us Denotementioning

confidence: 99%