Lp approximation problems in system identification with RBF neural networks are investigated.It is proved that by superpositions of some functions of one variable in Lploc(R),one can approximate continuous functionals defined on a compact subset of Lp(K) and continuous operators from a compact subset of Lp1(K1) to a compact subset of Lp2(K2).These results show that if its activation function is in Llpoc(R) and is not an even polynomial,then this RBF neural networks can approximate the above systems with any accuracy.
Lp approximation capability of radial basis function（RBF）neural networks is investigated.Ifg:R+1→R1 and g(‖x‖Rn)∈ L（loc）p（Rn）with 1≤p<∞,then the RBF neural networks with g as theactivation function can approximate any given function in Lp（K）with any accuracy for any compactset K in Rn,if and only if g（x）is not an even polynomial.
