We study weighted total least squares problems on infinite dimensional spaces. We present some necessary and sufficient conditions for the regularized problem to have a solution. The existence of solution can also be assured for the regularized minimization problem with a constraint to special subsets. Furthermore, we show that a regularization in infinite dimensional total least squares problems is necessary, since in most cases the problem without regularization does not admit a solution.

中文翻译：

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无限维空间上的总最小二乘问题

我们研究无限维空间上的加权总最小二乘问题。我们给出了正则化问题有解的一些充要条件。对于限制到特殊子集的正则化最小化问题，也可以保证解的存在。此外，我们表明无限维全最小二乘问题中的正则化是必要的，因为在大多数情况下，没有正则化的问题不存在解决方案。