关于多变量函数和流形的最优可视表达补注  

Remarks on Representation of Multivariate Functions or Cloud Data in Visualized Low-Dimensional Spaces

作　　者：宋健[1] SONG Jian(Chinese Academy of Engineering,Beijing 100190)

机构地区：[1]中国工程院,北京100190

出　　处：《系统科学与数学》2025年第1期1-4,共4页Journal of Systems Science and Mathematical Sciences

摘　　要：前时作者曾证明(宋健,2001),平方可积函数空间L_(2)(Ω)中任何函数f(Ω)或云大数据可用较少的单变量函数组合表达,得到梯度算子积分方程组.该方程组的本征元列构成给定f(Ω)特属的直交系、展成短和收敛快的级数.该补注表明,特属直交系是f(Ω)派生的正自伴算子的本征元列.It was proved previously that a given multivariate function or cloud data of L2(Ω)can be represented in form of short combination of one-dimentional functions as specific-private orthonormal system derived from a system of integral equations(Song,2001).These remarks show the said orthonormal system is just eigenfuctions of a positive self-adjoint operators spawned by the subject function itself in Hilbert Space.

关 键 词：多变量函数 分解 近似 FREDHOLM算子 自伴算子 特属直交系 强收敛 

分 类 号：O177[理学—数学]