Abstract
Positive homogeneous functions on R of a negative degree are characterized by a new counterpart of the Euler's homogeneous function theorem using quantum calculus and replacing the classical derivative operator by Jackson derivative. As application we start by characterizing the harmonic functions associated to Jackson derivative. Then, the solution of the Cauchy problem associated to the analogue of the Euler operator is given. Using this solution we study the associated nu-potential. Its Markovianity property is treated (C) 2017 Ivane Javakhishvili Tbilisi State University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license.