Interpolation and duality in algebras of multipliers on the ball

We study the multiplier algebras $A(\\mathcal{H})$ obtained as closure of polynomials on certain reproducing kernel Hilbert spaces $\\mathcal{H}$ ball $\\mathbb{B}\_d$ $\\mathbb{C}^d$. Our results apply, in particular, to Drury–Arveson space, Dirichlet space and Hardy ball. first obtain a complete description dual second $A(\\mathcal H)$ terms complementary bands Henkin totally singular measures for $\\operatorname{Mult}(\\mathcal{H})$. This is applied several definitive interpolation. In we establish sharp peak interpolation result compact $\\operatorname{Mult}(\\mathcal{H})$-totally null sets well Pick theorem. Conversely, show that mere set null.