Real-analytic finitely forcible kernels

Abstract

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

arXiv comment16 pages