On the Relative Φ-Growth of Hadamard Compositions of Dirichlet Series-Reference-Cited by-同舟云学术

On the Relative Φ-Growth of Hadamard Compositions of Dirichlet Series

Published:2024-07-19 Issue:7 Volume:13 Page:487
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Sheremeta Myroslav¹^ORCID,Mulyava Oksana²

Affiliation:

1. Department of Mechanics and Mathematics, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine

2. Department of Higher Mathematics, National University of Food Technologies, 01033 Kyiv, Ukraine

Abstract

For the Dirichlet series F(s)=∑n=1∞fnexp{sλn}, which is the Hadamard composition of the genus m of similar Dirichlet series Fj(s) with the same exponents, the growth with respect to the function G(s) given as the Dirichlet series is studied in terms of the Φ-type (the upper limit of MG−1(MF(σ))/Φ(σ) as σ↑A) and convergence Φ-class defined by the condition ∫σ0AΦ′(σ)MG−1(MF(σ))Φ2(σ)dσ<+∞, where MF(σ) is the maximum modulus of the function F at an imaginary line and A is the abscissa of the absolute convergence.

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/7/487/pdf

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