Zeros of Bernoulli-type functions and best approximations Original Research Article

The zero sets of (D+a)ng(t)(D+a)ng(t) with View the MathML sourceD=d/dt in the (t,a)(t,a)-plane are investigated for View the MathML sourceg(t)=teαt(et−1)−1 and View the MathML sourceg(t)=eθt(et+1)−1. The results are used to determine entire interpolations to functions View the MathML sourcex+ne−λx, which give representations for the best approximation and best one-sided approximation from the class of functions of exponential type η>0η>0 to View the MathML sourcex+ne−λx.