On belonging of entire Dirichlet series to a modified generalized convergence class
Journal Title: Математичні Студії - Year 2018, Vol 50, Issue 2
Abstract
For entire Dirichlet series F(s)=∑+∞n=0anesλn we found conditions on an, λn and on positive functions α and β continuous increasing to +∞ on [0,+∞) are found, under which the condition ∫+∞σ01β(σ)α(1σlnM(σ,F))dσ≤+∞ is equivalent to the condition ∑n=1+∞(α(λn)−α(λn−1))β1(1λnln1|an|)≤+∞ , where β1(x)=∫+∞xdtβ(t), and M(σ,F)=sup{|F(σ+it)|:t∈R}.
Authors and Affiliations
O. Mulyava
Keywords
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- EP ID EP525258
- DOI 10.15330/ms.50.2.135-142
- Views 70
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