Abstract
Let F be a non-empty closed subset of an open set Ω in N -dimensional Euclidean space ℝ N , where N ≥ 2. We shall give a survey of Runge and Walsh type theorems for better than uniform harmonic approximation on F and applications of these theorems to the study of growth and decay properties of entire harmonic and entire holo-morphic functions along rays, the classical Dirichlet problem, and the theory of the Radon transform.
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