INTERPOLATION PROBLEMS IN SEVERAL VARIABLES

We obtain a noncommutative Nudel'man type interpolation theorem in sev eral variables and a commutative analogue for H-infinity(B-n), the Har dy space of bounded analytic functions in the open ball of C-n. Using this result, we obtain an operatorial analogue in several variables of the Rosenblum-Rovnyak restriction theorem as well as an extension to the noncommutative analytic Toeplitz algebra F-infinity. We provide ne w extensions of the Caratheodory-Fejer and Nevanlinna-Pick interpolati on theorems for F-infinity. (C) 1998 Academic Press.