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Regularization methods for ill-posed problems in multiple Hilbert scales. (English) Zbl 1252.47010

An overview of the theory of regularization methods in Hilbert scales is presented. The concept of a multiple Hilbert scale on a product space is introduced, the regularization methods on these scales are defined, first for the case of a single observation and then for the case of multiple observations. Convergence results in Hilbert scales under special conditions are proved. The orders of convergence are derived. The problem of optimal convergence is studied and the optimal orders of convergence are obtained.

MSC:

47A52 Linear operators and ill-posed problems, regularization
45Q05 Inverse problems for integral equations
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