Logarithm of a Function, a Well-Posed Inverse Problem

• 作者: Denisse Guzmán Aguilar Silvia Reyes Mora Víctor A. Cruz Barriguete
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: LOGARITHM FUNCTION INVERSE PROBLEM STABILITY
• 年，卷（期）: 2014,（1）
• 页码范围: 1-5
• 页数: 5页
• 分类号: O1

摘要

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.