On the eigenvalues and eigenfunctions of some integral operators (Q1066402)

The authors study the eigenvalues and eigenfunctions of an integral operator \(T_{\tau}\) defined by \[ (T_{\tau}f)(x)=\int^{\tau}_{0}K(x-y)f(y)dy. \] Under some assumptions on the kernel K(x), it is shown that the operator \(T_{\tau}\) is continuous in \(\tau\) and that the eigenfunctions are continuous.