Interpolation Problems in Several Variables

We obtain a noncommutative Nudel’man type interpolation theorem in several variables and a commutative analogue for H` Bn., the Hardy space of bounded analytic functions in the open ball of Cn. 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`. We provide new extensions of the Carath´eodory]Fej´er and Nevanlinna]Pick interpolation theorems for F`.