Zeros of Bernoulli-type functions and best approximations

Abstract

The zero sets of ( D + a ) n g ( t ) with D = d / d t in the ( t , a ) -plane are investigated for g ( t ) = t e α t ( e t − 1 ) − 1 and g ( t ) = e θ t ( e t + 1 ) − 1 . The results are used to determine entire interpolations to functions x + n e − λ x , which give representations for the best approximation and best one-sided approximation from the class of functions of exponential type η > 0 to x + n e − λ x .