Study on spectral representation and eigenexpansion based on eigen-operators |
| |
Authors: | Hongyu WANG Tianshuang QIU |
| |
Affiliation: | Faculty of Electronic Information and Electrical Engineering,Dalian University of Technology,Dalian 116024,China |
| |
Abstract: | The spectral representation and expansion based on eigen-operators were deeply studied.The relations between Green’s function of characteristic differential equation and Hermitian differential and integral operators were given.The inverse relations between Hermitian differential operator and Hermitian integral operator were also studied.The spectral representation of Hermitian differential operators was given.It was also shown that the S-L eigen-equation cannot be used to realize the spectral representations of infinite dimensions in a finite interval.The method is much simpler and clearer than that of Neumann,and has advantages.The eigen-expansion (eigen-decomposition) of the Hermitian integral operator was given,which has the advantages of theoretical generality and comprehensiveness.The incorrect discussion in Wang et al2]was correct that it is used to study the representation of characteristic spectrum.The physical and geometric meanings of naming for the long spherical wave function in optimal eigen-expansion were given. |
| |
Keywords: | Green’s function S-L differential equation eigen-operator spectral representation eigen-expansion long spherical wave function |
|
| 点击此处可从《通信学报》浏览原始摘要信息 |
|
点击此处可从《通信学报》下载全文 |