An extension of the theory of Fredholm determinants (Q808396)

It is the aim of Fredholm's determinant theory to write the resolvent of an operator K as the quotient of an operator-valued entire function N(z) and a scalar-valued entire function d(z). This means that \[ (I-zK)^{- 1}=N(z)/d(z) \] for all z in the resolvent set. For certain integral operators occuring in the theory of dynamical systems, the author is looking for representations, where N(z) and d(z) have only a finite, but sufficiently large radius of convergence.