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Compositions of Dirichlet series similar to the Hadamard compositions, and convergence classes

Author
O. M. Mulyava1, M. M. Sheremeta2
1) Kyiv National University of Food Technologies; 2) Ivan Franko National University of Lviv
Abstract
Let (λn) be a positive sequence increasing to +, m2 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:C2C 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.
Keywords
Dirichlet series; convergence class; Hadamard composition
DOI
doi:10.15330/ms.51.1.25-34
Reference
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Pages
25-34
Volume
51
Issue
1
Year
2019
Journal
Matematychni Studii
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