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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/2504.00675 |
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| _version_ | 1866918131663896576 |
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| author | Fischer, Jan Ziebell, Jobst |
| author_facet | Fischer, Jan Ziebell, Jobst |
| contents | On normed vector spaces there is a well-known connection between the Tikhonov well-posedness of a minimisation problem and the differentiability of an associated convex conjugate function. We show how this duality naturally generalises to the setting of asymmetrically normed spaces and prove a universal differentiability property of the convex conjugate of the cumulant-generating function of a mean-zero measure on a locally convex space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00675 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tikhonov Well-Posedness and Differentiability on Asymmetrically Normed Spaces Fischer, Jan Ziebell, Jobst Functional Analysis On normed vector spaces there is a well-known connection between the Tikhonov well-posedness of a minimisation problem and the differentiability of an associated convex conjugate function. We show how this duality naturally generalises to the setting of asymmetrically normed spaces and prove a universal differentiability property of the convex conjugate of the cumulant-generating function of a mean-zero measure on a locally convex space. |
| title | Tikhonov Well-Posedness and Differentiability on Asymmetrically Normed Spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2504.00675 |