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为了使正交函数分析法成为一套建立在严格数学理论基础上、便于应用的较完整的分析法 ,在广义混合正交函数的基础上 ,提出了一类新的线性、连续、有界算子——分段广义正交多项式算子 (简称为 PGOPO) ,根据正交函数的性质及逼近论中的有关定理 ,对 PGOPO算子的基本性质进行了概括和总结 ;探讨了 PGOPO算子逼近下的误差及收敛性问题 ,为正交函数分析法初步建立了一个合适的数学框架 ,从而使现有的正交函数分析法系统化、理论化 ,并为下一步推广 PGOPO方法在控制理论中的运用提供理论基础
In order to make Orthogonal Function Analysis a set of more complete analytic methods based on rigorous mathematical theory and easy to apply, a new kind of linear, continuous, bounded arithmetic is proposed on the basis of generalized mixed orthogonal functions Based on the properties of orthogonal functions and the related theorems in approximation theory, the basic properties of PGOPO operators are summarized and summarized. The relations between PGOPO operator approximation Under the error and convergence problem, an appropriate mathematical framework is established for the orthogonal function analysis method so that the existing orthogonal function analysis method can be systematized and theorized. In the next step, the generalization of PGOPO method in control theory Provide the theoretical basis for the use of