A Functorial Approach to Multi-Space Interpolation with Function Parameters
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918295028891648 |
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| author | Lamby, Thomas Nicolay, Samuel |
| author_facet | Lamby, Thomas Nicolay, Samuel |
| contents | We introduce an extension of interpolation theory to more than two spaces by employing a functional parameter, while retaining a fully functorial and systematic framework. This approach allows for the construction of generalized intermediate spaces and ensures stability under natural operations such as powers and convex combinations. As a significant application, we demonstrate that the interpolation of multiple generalized Sobolev spaces yields a generalized Besov space. Our framework provides explicit tools for handling multi-parameter interpolation, highlighting both its theoretical robustness and practical relevance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12572 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Functorial Approach to Multi-Space Interpolation with Function Parameters Lamby, Thomas Nicolay, Samuel Functional Analysis Numerical Analysis 46B70, 46M35, 46E35, 46E99 We introduce an extension of interpolation theory to more than two spaces by employing a functional parameter, while retaining a fully functorial and systematic framework. This approach allows for the construction of generalized intermediate spaces and ensures stability under natural operations such as powers and convex combinations. As a significant application, we demonstrate that the interpolation of multiple generalized Sobolev spaces yields a generalized Besov space. Our framework provides explicit tools for handling multi-parameter interpolation, highlighting both its theoretical robustness and practical relevance. |
| title | A Functorial Approach to Multi-Space Interpolation with Function Parameters |
| topic | Functional Analysis Numerical Analysis 46B70, 46M35, 46E35, 46E99 |
| url | https://arxiv.org/abs/2601.12572 |