The Index of the Complex Eigenvalues of a Parity Progressive Population Operator1

In this paper we discuss the index of the complex eigenvalue of a parity progressive population operator.Under certain conditions, we first prove that all the complex eigenvalues of this operator, except at most finitely many ones, are of index 1, and then, as an application of this result, we obtain the asymptotic expansion ofthe solution of the corresponding parity progressive population equation