Research On Correlation Problems Of Two-parameter N-th Order α -Times Integrated C -Semigroups

Semigroups theory of linear operators in Banach space is one of the important tools to solve functional analysis problems.In 2014,Mingcui Zhang and Xiaoqiu Song et.al.were introduced the concept of one-parameter n-th orderα-times integrated C-semigroups and studied some related properties about it.Using the research method of classical operator semigroup related knowledge and the discussion method of two parameter C-semigroups,according to the basic knowledge of one-parameter n-th orderα-times integrated C-semigroups,the theoretical knowledge of one-parameter n-th orderα-times integrated C-semigroups is extended to two-parameter n-th orderα-times integrated C-semigroups.The concepts of the two-parameter n-th orderα-times integrated C-semigroups.This dissertation is mainly composed of the following two parts:The first aspect:Based on the research methods of two-parameter C-semigroups and n-times integrated C-semigroups,and the theoretical knowledge of one-parameter n-th orderα-times integrated C-semigroups,the basic concept,pre-solution set,spectrum,sub-generating element and infinitesimal generator of the two-parameter n-th orderα-times integrated C-semigroups are studied,and the classification is based on the existence of(λ^n-1μ^n-1（aλ+bμ）ⁿ-T（t,s）)^-1)the spectrum;The second aspect:Based on the basic knowledge of the second chapter of two parameter n-th orderα-times integrated C-semigroups,the approximation（Yosida approximation）,exponential boundedness,pre-solution equation and basic properties of the two-parameter n-orderα-times integrated C-semigroups are discussed by using the research method of two parameter C-semigroups theory.