An extension of Mercer's theory to \(L^p\) (Q1928541)

The paper consist of four sections. In Section 1, the author considers an integral operator generated by a Mercer like kernel \(K\). In Section 2, Mercer's theory is extended to the convergence in the \(p\)-mean under suitable assumptions. Further, a series representations on the convergence in the \(p\)-mean of functions, in the range of a generalized power of the operator, and a recovery formula is obtained. The spectral properties of a modified version of an integral operator acting on \(L^p(X,v)\) in Section 4 is used to estimate the approximation numbers.