Meromorphic interpolation in several variables Original Research Article

We obtain a multivariable Nudel’man type interpolation theorem for meromorphic operators on Fock spaces and for operator-valued meromorphic functions on the open unit ball of image (ngreater-or-equal, slanted1). As consequences, we provide new Carathéodory–Fejér, Nevanlinna–Pick type interpolation results, and Rosenblum–Rovnyak type restriction theorem for meromorphic operators. In the particular case when n=1, our indefinite generalization of Nudel’man’s theorem provides new interpolation results for meromorphic functions having a finite number of poles in the open unit disc.