平方可积函数解析分解的构造性证明

Constructive proof about quadratic integrable function decomposition into analytic function

中文关键词  解析  调和函数  Lebesgue可积函数

英文关键词  analytic  harmonic function  Lebesgue integrable

中文摘要

      在H_∞控制理论及应用其理论进行设计中,经常用到结论:在虚轴上定义的平方可积函数分别与在开左、右半平面解析且一致平方可积函数的相互对应关系.但由于此结果的证明较多地用到不同学科的数学结论,故很难找到其详尽的证明.应用构造性方法,找出了它们间相互对应的数学表达式,并详细证明了这个表达式的准确性,证明了这种关系是一一对应的.

英文摘要

      In H-infinity control theory and control system design with the theory,the quadratic integration function defined on imaginary axis is often decomposed into analytic functions on right half-plane and left half-plane respectively.However,there is no strict proof because of the conclusion using many mathematic theories in different subject.A one-to-one connection among these functions is established and proved in detail.