LAPLACE-STIELTJES变换所定义的解析函数的下级

LAPLACE-STIELTJES变换所定义的解析函数的下级 LOWER ORDERS OF THE ANALYTIC FUCTIONS DEFINED BY LAPLACE STIETJES TRANSFORMS 尤秀英 Yiu Xiuying 1 first-author 武汉大学数学系 武汉大学数学系 Department of Mathematics,Wuhan University Department of Mathematics,Wuhan University 对于Ｌａｐｌａｃｅ－Ｓｔｉｅｌｔｊｅｓ变换所定义的整函数或在半平面内解析的函数，分别定义了下级，适当引进序列０≤λｎ↑＋∞，建立该变换的最大模与“最大项”之间的关系，并由这些关系推导了两类下级的充分必要条件 For the entire function or the analytic function in a half plane represented by a Laplace Stieltjes transform F（s）=∫ +∞ 0 e -st d α（x）（s=σ+ i t,σ,t∈R）,the lowet order is defined.We introduce a sequence 0≤λ n↑+∞,define the "maximam term"of the transtorm,establish the relations between the maximum modulus and the maximum term and deduce from them the necessary and sufficient conditions of the lower orders which are extensions of the corresponding results of Dirichlet series. 收敛横坐标 收敛半平面 最大模 最大项 下级 abscissa of convergence half plane of convergence maximam modulus maximum term lower order O177.4 1997-05-01 2021-04-01 5