Vector-Valued Functions Generated by the Operator of Finite Order and Their Application to Solving Operator Equations in Locally Convex Spaces

作     者：Man'ko, S. N. 

作者机构：Orel State Inst Culture Ul Leskova 15 Oryol 302020 Russia 

出 版 物：《RUSSIAN MATHEMATICS》 (俄罗斯数学)

年 卷 期：2018年第62卷第3期

页      面：34-44页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：locally convex space order and type of operators vector-valued functions differential-operator equation 

摘      要：This work is devoted to solving some classes of operator equations, based on the solution of auxiliary one-parameter family of equations, which is obtained fromthe original operator equation by formal replacement of the operator of the integrated parameter. Solutions are vector-valued functions represented by power series or integral. We investigate some properties of these solutions, namely, growth characteristics, the domain of analyticity. The investigation is realized by means of order and type of operator, operator order and operator type of the vector relative to the operator.