Logarithm of a Function, a Well-Posed Inverse Problem ()
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.
Share and Cite:
Mora, S. , Barriguete, V. and Aguilar, D. (2014) Logarithm of a Function, a Well-Posed Inverse Problem.
American Journal of Computational Mathematics,
4, 1-5. doi:
10.4236/ajcm.2014.41001.
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