Logarithm of a Function, a Well-Posed Inverse Problem


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, its 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.

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S. Mora, V. Barriguete and D. Aguilar, "Logarithm of a Function, a Well-Posed Inverse Problem," American Journal of Computational Mathematics, Vol. 4 No. 1, 2014, pp. 1-5. doi: 10.4236/ajcm.2014.41001.

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