Study on spectral representation and eigenexpansion based on eigen-operators
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 Hermiti...
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| Format: | Article |
| Language: | zho |
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Editorial Department of Journal on Communications
2020-05-01
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| Series: | Tongxin xuebao |
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| Online Access: | http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2020096/ |
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| _version_ | 1841539323044823040 |
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| author | Hongyu WANG Tianshuang QIU |
| author_facet | Hongyu WANG Tianshuang QIU |
| author_sort | Hongyu WANG |
| collection | DOAJ |
| description | 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 al<sup>[2]</sup>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. |
| format | Article |
| id | doaj-art-0696a51eb7af4c5984665092916af6a0 |
| institution | Kabale University |
| issn | 1000-436X |
| language | zho |
| publishDate | 2020-05-01 |
| publisher | Editorial Department of Journal on Communications |
| record_format | Article |
| series | Tongxin xuebao |
| spelling | doaj-art-0696a51eb7af4c5984665092916af6a02025-01-14T07:19:14ZzhoEditorial Department of Journal on CommunicationsTongxin xuebao1000-436X2020-05-01411859735237Study on spectral representation and eigenexpansion based on eigen-operatorsHongyu WANGTianshuang QIUThe 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 al<sup>[2]</sup>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.http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2020096/Green’s functionS-L differential equationeigen-operatorspectral representationeigen-expansionlong spherical wave function |
| spellingShingle | Hongyu WANG Tianshuang QIU Study on spectral representation and eigenexpansion based on eigen-operators Tongxin xuebao Green’s function S-L differential equation eigen-operator spectral representation eigen-expansion long spherical wave function |
| title | Study on spectral representation and eigenexpansion based on eigen-operators |
| title_full | Study on spectral representation and eigenexpansion based on eigen-operators |
| title_fullStr | Study on spectral representation and eigenexpansion based on eigen-operators |
| title_full_unstemmed | Study on spectral representation and eigenexpansion based on eigen-operators |
| title_short | Study on spectral representation and eigenexpansion based on eigen-operators |
| title_sort | study on spectral representation and eigenexpansion based on eigen operators |
| topic | Green’s function S-L differential equation eigen-operator spectral representation eigen-expansion long spherical wave function |
| url | http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2020096/ |
| work_keys_str_mv | AT hongyuwang studyonspectralrepresentationandeigenexpansionbasedoneigenoperators AT tianshuangqiu studyonspectralrepresentationandeigenexpansionbasedoneigenoperators |