A Functorial Approach to Multi-Space Interpolation with Function Parameters
Functional Analysis
2026-01-21 v1 Numerical Analysis
Numerical Analysis
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.
Cite
@article{arxiv.2601.12572,
title = {A Functorial Approach to Multi-Space Interpolation with Function Parameters},
author = {Thomas Lamby and Samuel Nicolay},
journal= {arXiv preprint arXiv:2601.12572},
year = {2026}
}