Interpolation Formulas for Harmonic Functions Original Research Article

It is known that a real-valued entire harmonic functionuof exponential type less thanπis uniquely determined by its values at the pointsnandneiα,n=0, ±1, ±2, …, unlessαis a rational multiple ofπ. Forα=π/2, which belongs to the exceptional cases, Ching has proved thatuis uniquely determined by its values at these points ifuis in addition an odd function. In the present paper we shall extend this result to the caseα=(2k+1)π/(2l), wherekandl≠0 are arbitrary integers. Furthermore, we shall present formulas which allow a reconstruction of real-valued entire harmonic functions of exponential typeπby their samples at the pointsnandneiα,n=0, ±1, ±2, …, whenα=(2k+1)π/(2l) or whenα/πis irrational and algebraic.