TITLE:
Logarithm of a Function, a Well-Posed Inverse Problem
AUTHORS:
Silvia Reyes Mora, Víctor A. Cruz Barriguete, Denisse Guzmán Aguilar
KEYWORDS:
Logarithm Function; Inverse Problem; Stability
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.4 No.1,
January
22,
2014
ABSTRACT: It poses the
inverse problem that consists in finding the logarithm of a function. It shows
that when the function is holomorphic in a simply connected domain , the solution at the inverse problem exists and is unique if a
branch of the logarithm is fixed. In addition, it’s demonstrated that when the function is
continuous in a domain , where is Hausdorff space and
connected by paths. The solution of the problem exists and is unique if a branch of the logarithm is
fixed and is stable; for what in this case, the inverse problem turns out to be well-posed.