On Dirichlet series similar to Hadamard compositions in half-plane - Bandura, A.I.; Mulyava, O.M.; Sheremeta, M.M. (Carpathian Mathematical Publications, 2023)
Let F(s)=_n=1^∞a_n{sλ_n} and F_j(s)=_n=1^∞a_n,j{sλ_n}, j=1,p, be Dirichlet series with exponents 0λ_n+∞, n→∞, and the abscissas of absolutely convergence equal to 0. The function F is called Hadamard composition of the genus m1 of the functions F_j if a_n=P(a_n,1,… ,a_n,p), where P(x_1,… ,x_p)=_k_1+…+k_p=mc_k_1… k_px_1^k_1… x_p^k_p is a homogeneous polynomial of degree m. In terms of generalized orders and convergence classes the connection between the growth of the functions F_j and the growth of the Hadamard composition F of the genus m1 of F_j is investigated. The pseudostarlikeness and pseudoconvexity of the Hadamard composition of the genus m1 are studied.