Complex-order scale-invariant operators and self-similar processes
Arash Amini, Sharif University, Tehran, Iran

Meeting • 21 August 2018

Abstract
The scale-invariant operators are those that translate input dilation into the same dilation of the output. Typical examples are the ordinary derivative operators. It is interesting that the complete family of linear shift-invariant operators (filters) that are also scale-invariant is known. The family could be considered as the generalisation of the nth-order derivation to zth-order derivation where z is a complex number. In this talk, I will introduce this family, their inverse and adjoint operators, and their properties. Finally, I will discuss about how these operators can be applied to certain white noise processes to generate self-similar processes.