INTERPOLATING FUNCTIONS OF MINIMAL NORM, STAR-INVARIANT SUBSPACES, AND KERNELS OF TOEPLITZ-OPERATORS

It is proved that for each inner function theta there exists an interpolating sequence {z(n)} in the disk such that sup(n)\theta\(z(n))\ < 1, but every function g in H infinity with g(z(n)) = theta(z(n)) (n = 1, 2, ... ) satisfies \\g\\ infinity greater-than-or-equal-to 1. Some results are obtained concerning interpolation in the star-invariant subspace H-2 - theta H-2 . This paper also contains a "geometric" result connected with kernels of Toeplitz operators.