Differentiable Peak‐Interpolation on Bounded Domains with Smooth Boundary

Let D be a bounded domain in C n with C 2 boundary, and, for 1 ⩽ k ⩽ ∞, let A k ( D ) be the algebra of functions holomorphic on D and C k on a neighbourhood of D ¯ . It is shown that each peak‐interpolation set for A k ( D ) is a finite set.