Interpolation and duality in algebras of multipliers on the ball.

We study the multiplier algebras A.H/obtained as the closure of the polynomials on certain reproducing kernel Hilbert spaces H on the ball Bd of Cd. Our results apply, in particular, to the Drury-Arveson space, the Dirichlet space and the Hardy space on the ball. We first obtain a complete description of the dual and second dual spaces of A.H/in terms of the complementary bands of Henkin and totally singular measures for Mult.H/. This is applied to obtain several definitive results in interpolation. In particular, we establish a sharp peak interpolation result for compact Mult.H/-totally null sets as well as a Pick and peak interpolation theorem. Conversely, we show that a mere interpolation set is Mult.H/-totally null. [ABSTRACT FROM AUTHOR]