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arXiv · 2608.22778

Real-analytic finitely forcible kernels

Junchi Zhang
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Abstract

Lovász and Szegedy asked whether a nonconstant continuous, or even smooth, finitely forcible kernel exists. For every $0<λ\leq1/128$, we construct an explicit nonconstant real-analytic kernel $W_λ$ taking values in $(1/4,7/8)$. A single finite family of simple graphs, independent of $λ$, forces every $W_λ$ among all bounded symmetric real-valued kernels on $[0,1]^2$.

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Junchi Zhang. 2026-08-24. Real-analytic finitely forcible kernels. https://arxiv.org/abs/2608.22778

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