Representation of entire harmonic functions by given values (Q1076846)

The authors establish a new interpolation formula that represents an entire harmonic function of exponential type \(\sigma\) less than \(\pi\) in terms of u(n) and \(u(n+i)\), provided that both u(n) and \(u(n+i)\) are \(O(\exp (| n| /(\log | n|)^{\gamma}),\) \(\gamma >1\). As a corollary they deduce that if u is bounded by K at the points n and \(n+i\), then u is bounded by KM in every strip \(| Im z| \leq y_ 0\), where M depends only on \(\sigma\) and \(y_ 0\).