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arXiv · 2601.12572

A Functorial Approach to Multi-Space Interpolation with Function Parameters

Thomas Lamby·Samuel Nicolay
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Abstract

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.

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Thomas Lamby, Samuel Nicolay. 2026-01-18. A Functorial Approach to Multi-Space Interpolation with Function Parameters. https://arxiv.org/abs/2601.12572

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