Mazzieri, Gisela L.; Spies, Ruben D. Regularization methods for ill-posed problems in multiple Hilbert scales. (English) Zbl 1252.47010 Inverse Probl. 28, No. 5, Article ID 055005, 30 p. (2012). 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. Reviewer: Denis Sidorov (Irkutsk) Cited in 1 Document MSC: 47A52 Linear operators and ill-posed problems, regularization 45Q05 Inverse problems for integral equations Keywords:inverse problem; ill-posed problem; Hilbert scale; Tikhonov regularization PDFBibTeX XMLCite \textit{G. L. Mazzieri} and \textit{R. D. Spies}, Inverse Probl. 28, No. 5, Article ID 055005, 30 p. (2012; Zbl 1252.47010) Full Text: DOI arXiv