给出右半平面解析的Laplace-Stieltjes变换的广义级与广义型的定义,研究了最大模M_u(σ,F)=sup{|∫_0~x e~(-(σ+it)y)dv(y)|:x∈(0,+∞),t∈R},最大项μ(σ,F)=max_(n∈N){A_n~*e~(-λnσ)},最大项指标v(σ,F)=max_k{λ_k|μ(σ,F)=A_k~*e~(-λkσ)}及其系数之间的关系,推广了Dirichlet级数的相关结果.
We define the generalized orders and generalized types of Laplace-Stieltjes transforms which convergence in the right half-plane.Some interesting relationships on the maximum modulus M_u(σ,F) = sup{|∫_0~x e~(-(σ+it)y)dv(y)|:x ∈(0,+∞),t ∈ R},the maximum term μ(σ,F) = max_(n∈N){A_n~*e~(-λnσ)},the index of maximum term v(σ,F) =max_k{λ_k|μ(σ,F) = A_k~*e~(-λkσ)} and the coefficients of such transforms are obtained,which briefly extend some results of Dirichlet series.