ON SEVERAL ASPECTS OF J-INNER FUNCTIONS IN SCHUR ANALYSIS

The aim of this paper is to give a presentation of several subjects of Schur analysis with some historical information. The class of J-inner functions plays a key role in this new mathematical field which is si tuated at the seam of various mathematical disciplines (operator theor y, scattering theory, complex function theory, prediction theory for s tochastic processes, spectral theory for differential operators). This article shows the importance of J-inner functions in Schur analysis. We shall concentrate on the Soviet roots of the theory and discuss Pot apov's factorization theory and Arov's investigations on Darlington sy nthesis. Furthermore Rie present some of Arov's results on interrelati ons between a certain subclass of J-inner functions and generalized bi tangential Schur-Nevanlinna-Pick interpolation.