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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.06506 |
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| _version_ | 1866908308584005632 |
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| author | Fischbacher, Christoph Gesztesy, Fritz Littlejohn, Lance L. |
| author_facet | Fischbacher, Christoph Gesztesy, Fritz Littlejohn, Lance L. |
| contents | This largely pedagogical paper recalls some facts on defect numbers of products of closed operators employing results from the theory of semi-Fredholm operators and then applies these facts to positive integer powers of symmetric operators and subsequently to certain minimal Sturm--Liouville and minimal higher even-order ordinary and partial differential operators. We also point out some unexpected missed opportunities when comparing the work of different groups on this subject. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some Remarks on the Product Formula for Defect Numbers of Closed Operators Fischbacher, Christoph Gesztesy, Fritz Littlejohn, Lance L. Functional Analysis Mathematical Physics Primary: 47A05, 47A53. Secondary: 47B02, 47E05, 47F05 This largely pedagogical paper recalls some facts on defect numbers of products of closed operators employing results from the theory of semi-Fredholm operators and then applies these facts to positive integer powers of symmetric operators and subsequently to certain minimal Sturm--Liouville and minimal higher even-order ordinary and partial differential operators. We also point out some unexpected missed opportunities when comparing the work of different groups on this subject. |
| title | Some Remarks on the Product Formula for Defect Numbers of Closed Operators |
| topic | Functional Analysis Mathematical Physics Primary: 47A05, 47A53. Secondary: 47B02, 47E05, 47F05 |
| url | https://arxiv.org/abs/2504.06506 |