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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.24512 |
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| _version_ | 1866916976414162944 |
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| author | Massopust, Peter R. |
| author_facet | Massopust, Peter R. |
| contents | In this paper, we introduce fractal interpolation on complete semi-vector spaces. This approach is motivated by the requirements of preservation of positivity or monotonicity of functions for some models in approximation and interpolation theory. The setting in complete semi-vector spaces does not requite additional assumptions but is intrinsically built into the frame work. For the purposes of this paper, fractal interpolation in the complete semi-vector spaces $C^+$ and $L_p^+$ is considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24512 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi-Rings, Semi-Vector Spaces, and Fractal Interpolation Massopust, Peter R. Functional Analysis In this paper, we introduce fractal interpolation on complete semi-vector spaces. This approach is motivated by the requirements of preservation of positivity or monotonicity of functions for some models in approximation and interpolation theory. The setting in complete semi-vector spaces does not requite additional assumptions but is intrinsically built into the frame work. For the purposes of this paper, fractal interpolation in the complete semi-vector spaces $C^+$ and $L_p^+$ is considered. |
| title | Semi-Rings, Semi-Vector Spaces, and Fractal Interpolation |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2509.24512 |