Relative growth of Hadamard compositions of entire Dirichlet  series

Oksana Mulyava, Myroslav Sheremeta, Yuriy Trukhan

Анотація


Let F(s)=∑n=1∞an exp{sλn} and Fj(s)=∑n=1∞an,jexp{sλn} be entire Dirichlet series with exponents 0≤λn↑+∞. The function F is called Hadamard composition of the genus m≥1 of the functions Fj if an=P(an,1,...,an,p), where P(x1,...,xp)=∑k1+...+kp=mck1... kpx1k1...xpkp is a homogeneous polynomial of degree m≥1. The growth of the function F with respect to the entire Dirichlet series G(s)=∑n=1∞gn exp{sλn} is identified with the growth of the function M-1G(MF(σ)), where MF(σ)=sup{|F(σ+it)|: t∈ ℝ}. The dependence of the growth of a function M-1G(MF(σ)) on the growth of functions M-1G(MFj(σ)) is studied in terms of generalized orders and a generalized convergence class.


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DOI: http://dx.doi.org/10.30970/vmm.2023.95.083-093

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