A new symmetric differential operator of normalized functions with applications in image processing

Abstract

Recently, a symmetric differential operator (SDO) is attracted to studying in the field of mathematical analysis. A new formal of SDO is presented to generalize some well known differential operators in a complex domain. According to this formulation, we shall exam the boundedness and compactness of this operator in complex spaces, such as Hilbert space and Sobolev space. For this purpose, we suggest new norms to solve the fractional Beltrami equation in the open unit disk. This operator has ability to depict the analytic geometric representation of the solution of second order differential equation utilizing the concept of Schwarzian derivative in the open unit disk. Applications in imagings are given the sequel.