Estimates of entire functions of exponential type less than pi in terms of logarithmic sums over real Duffin and Schaeffer sequences

摘要

We give uniform estimates of entire functions of exponential type less than p having sufficiently small logarithmic sums over real sequences {lambda(n)} satisfying lambda(n)-n less than or equal to L and lambda(n+1)-lambda(n)greater than or equal todelta for fixed positive constants L and delta. We thereby generalize results about logarithmic sums over the set of integers and so-called relatively h-dense sequences. [References: 10]