Compositions of Dirichlet series similar to the Hadamard compositions, and convergence classes |
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Author |
info@nuft.edu.ua1, m_m_sheremeta@gmail.com2
1) Kyiv National University of Food Technologies; 2) Ivan Franko National University of Lviv
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Abstract |
Let (λn) be a positive sequence increasing to +∞, m≥2 and Dirichlet series
Fj(s)=∑∞n=0an,jexp{sλn} (j=1,2,…,m) have the abscissa A∈(−∞,+∞] of absolute
convergence. We say that Dirichlet series F(s)=∑∞n=0anexp{sλn} is similar to Hadamard compositions of of
Dirichlet series Fj if an=w(an,1,an,2) for all n, where w:C2→C is some function. Clearly, if w(an,1,an,2)=an,1an,2 then F is the Hadamard composition of the functions F1 and F2.
In the case |an|≍∏mj=1|an,j|ωj as n→+∞, where ωj>0 and
∑mj=1ωj=1, it is investigated the belonging of F to some convergence class with respect of the belonging to this class of functions Fj.
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Keywords |
Dirichlet series; convergence class; Hadamard composition
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DOI |
doi:10.15330/ms.51.1.25-34
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Reference |
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Pages |
25-34
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Volume |
51
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Issue |
1
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Year |
2019
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Journal |
Matematychni Studii
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Full text of paper | |
Table of content of issue |