Estimates of Entire Functions of Exponential Type Less than π in Terms of Logarithmic Sums over Real Duffin and Schaeffer Sequences

We give uniform estimates of entire functions of exponential type less than π having sufficiently small logarithmic sums over real sequences λn satisfying |λn−n|≤L and λn+1−λn≥δ for fixed positive constants L and δ. We thereby generalize results about logarithmic sums over the set of integers and so-called relatively h-dense sequences.