The class of differential expressions in with the integral boundary conditions
is considered, with and . Suppose that the boundary conditions are regular, i.e., one of the following conditions is satisfied: ; and ; and ; , and . As usual, the linear operator on is associated with , where the domain of is .
It is shown that is the generator of an analytic semigroup of bounded linear operators on . The detailed proof uses the usual techniques of the location of the spectrum and estimates on the resolvent as an integral operator with the Green function as kernel.