CLASS OF ADMISSIBLE PERTURBATIONS OF SPECIAL EXPRESSIONS INVOLVING COMPLETELY MONOTONIC FUNCTIONS

In this article, a class M-2 of admissible perturbations of the special expression M-0 = Sigma(r)(k=0) c(k)t(alpha k) D-t(rho k) in the weighted space L-omega(2)([1, infinity)) will be presented. It will be shown that the operator omega M-1/2(2)omega(-1/2), where omega belongs to the family of completely monotonic functions, is an admissible perturbation of M-0 in the non-weighted space L-2([1, infinity)), and eventually preserves the essential spectrum and nullity of M-0 in that space. Our discussion will be limited only to special expressions with alpha(1) < rho(1).