Strictly Decentralized Adaptive Estimation of External Fields using Reproducing Kernels

The paper’s Theorem 2 asserts the local squared-norm rate and a fused rate stated for the non-squared norm with exponent 2p, but the printed proof is only a sketch and even contains unresolved cross-references (“Theorem ?? and Corollary ??”), so the argument is incomplete in this version of the PDF . The candidate solution supplies the missing energy/Grönwall details and correctly derives the local squared-norm rate using the RKHS restriction–extension framework and the power function bound (leveraging properties summarized in the paper) , . However, it then claims an “equivalent” fused bound of order h^{2p} for the non-squared norm after proving a bound of that order for the squared norm—this “equivalence” is not correct (the non-squared norm would scale like h^p if the squared norm scales like h^{2p}). Thus, the model’s derivation is essentially right up to the last line, but the final equivalence statement over-claims the rate, paralleling the same notational/slip in the paper’s fused bound , .