  The fundamental theorem on commutant lifting due to Sarason does not carry
over to the setting of the polydisc. This paper presents two classifications of
commutant lifting in several variables. The first classification links the
lifting problem to the contractivity of certain linear functionals. The second
one transforms it into nonnegative real numbers. We also solve the
Nevanlinna-Pick interpolation problem for bounded analytic functions on the
polydisc. Along the way, we solve a perturbation problem for bounded analytic
functions. Commutant lifting and interpolation on the polydisc solve two
well-known problems in Hilbert function space theory.
