UNIQUENESS THEOREMS FOR HARMONIC FUNCTIONS
Abstract: In [3] we proved some uniqueness theorems for entire analytic functions f of exponential type which state that f must vanish identically or be a certain special function if f and certain derivatives of f vanish at the integers and the type of f is not too big. In this paper we prove analogous theorems for entire harmonic functions u of exponential type, where u and certain partial or directional derivatives vanish at the integers of two parallel lines or of two lines making an angle that is not a rational multiple of π. Our theorems generalize a result of Boas in [2],