Composition operators and a pull-back measure formula

A pull-back measure formula obtained in some particular cases by E. A. Nord gren and this author is generalized in the framework of boundary measures f or zero-free Nevanlinna class functions on the unit polydisk. The formula i s used to characterize the zero-free Nevanlinna class functions which are s olutions of Schroder's equation induced by a polydisk automorphism phi (i.e . to determine the zero-free functions f belonging to the Nevanlinna class which are solutions of the functional equation f omicron phi = lambdaf, for some constant lambda), thus generalizing earlier results obtained by R. Mo rtini and this author.