Abstract
In general, the problem of solving linear operator equations with a singular linear operator is ill-posed, if one includes the operator in the data. We give sufficient conditions on the perturbations in the operator and the right-hand side that guarantee stability of solutions. With different techniques we treat the cases that the linear operator is a Fredholm operator with index zero and that the linear operator is compact.KeywordsLinear OperatorGeneralize InverseFredholm OperatorSingular SystemLinear ManifoldThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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