The degree of ill-posedness for some composition governed by the Cesaro operator
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914646984753152 |
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| author | Deng, Yu Fischer, Hans-Jürgen Hofmann, Bernd |
| author_facet | Deng, Yu Fischer, Hans-Jürgen Hofmann, Bernd |
| contents | In this article, we consider the singular value asymptotics of compositions of compact linear operators mapping in the real Hilbert space of quadratically integrable functions over the unit interval. Specifically, the composition is given by the compact simple integration operator followed by the non-compact Ces`aro operator possessing a non-closed range. We show that the degree of ill-posedness of that composition is two, which means that the Ces`aro operator increases the degree of illposedness by the amount of one compared to the simple integration operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11411 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The degree of ill-posedness for some composition governed by the Cesaro operator Deng, Yu Fischer, Hans-Jürgen Hofmann, Bernd Numerical Analysis Functional Analysis 47A52 (Primary), 47B06, 65J20, 40G05 (Secondary) In this article, we consider the singular value asymptotics of compositions of compact linear operators mapping in the real Hilbert space of quadratically integrable functions over the unit interval. Specifically, the composition is given by the compact simple integration operator followed by the non-compact Ces`aro operator possessing a non-closed range. We show that the degree of ill-posedness of that composition is two, which means that the Ces`aro operator increases the degree of illposedness by the amount of one compared to the simple integration operator. |
| title | The degree of ill-posedness for some composition governed by the Cesaro operator |
| topic | Numerical Analysis Functional Analysis 47A52 (Primary), 47B06, 65J20, 40G05 (Secondary) |
| url | https://arxiv.org/abs/2401.11411 |