k tk|f(zk)| < ∞, then f ≡ 0 for every f ∈ F . Theorems of such kind arise in various applications: operator theory [Ni], approximation theory [Kh], [E3], sampling, etc. They are also of independent interest. We shall consider the case when G is the unit disk D = {|z| < 1}, |zk| → 1 as k → ∞, and F is the class H(D) of bounded holomorphic functions in D… (More)