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OF THE FIRST AND SECOND KINDS UNDER PERTURBATION OF THE OPERATOR WITH RANK CHANGE

Heinz W. Engl

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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.

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What this paper is about

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.

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Available 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.

Key concepts: Operator (biology), Shift operator, Mathematics, Finite-rank operator, Semi-elliptic operator, Linear map, Compact operator, Quasinormal operator

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