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We study the multiplier algebras $A(\mathcal{H})$ obtained as the closure ofthe polynomials on certain reproducing kernel Hilbert spaces $\mathcal{H}$ onthe ball $\mathbb{B}_d$ of $\mathbb{C}^d$. Our results apply, in particular, tothe 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$A(\mathcal H)$ in terms of the complementary bands of Henkin and totallysingular measures for $\operatorname{Mult}(\mathcal{H})$. This is applied toobtain several definitive results in interpolation. In particular, we establisha sharp peak interpolation result for compact$\operatorname{Mult}(\mathcal{H})$-totally null sets as well as a Pick and peakinterpolation theorem. Conversely, we show that a mere interpolation set is$\operatorname{Mult}(\mathcal{H})$-totally null.

Interpolation and duality in algebras of multipliers on the ball