Mellin Analysis and its distance concept. Applications to sampling   theory
  In this paper a notion of functional "distance" in the Mellin transform setting is introduced and a general representation formula is obtained for it. Also, a determination of the distance is given in terms of Lipschitz classes and Mellin-Sobolev spaces. Finally applications to approximate versions of certain basic relations valid for Mellin band-limited functions are studied in details. 
Carlo Bardaro, Paul L. Butzer, Ilaria Mantellini, Gerhard Schmeisser
math.FA