The Koornwinder--Kostenko--Teschl Conjecture for Jacobi Polynomials and the Discrete Laguerre Phase Transition

What the math gives to ML

The paper proves a sharp, dimension-free sup-norm bound for a carefully normalized Jacobi-polynomial feature, together with decay guarantees for a related discrete Laguerre evolution. The transferable asset is the normalization that makes every feature uniformly bounded by an explicit degree- and parameter-dependent constant. This can support polynomial positional or spectral features whose amplitudes cannot grow with degree, reducing activation and gradient instability compared with raw polynomial expansions. The most direct test is a Jacobi-feature layer replacing unbounded learned polynomial embeddings or high-degree spectral filters.