Regularization methods for ill-posed problems in multiple Hilbert scales

MAZZIERI, GISELA L; SPIES, RUBÉN D

INVERSE PROBLEMS

IOP PUBLISHING LTD

Lugar: Londres; Año: 2012 vol. 28 p. 1 - 30

0266-5611

Several convergence results in Hilbert scales under different source conditionsare proved and orders of convergence and optimal orders of convergenceare derived. Also, relations between those source conditions are proved. Theconcept of a multiple Hilbert scale on a product space is introduced, andregularization methods on these scales are defined, both for the case of a singleobservation and for the case of multiple observations. In the latter case, it isshown how vector-valued regularization functions in these multiple Hilbertscales can be used. In all cases, convergence is proved and orders and optimalorders of convergence are shown. Finally, some potential applications and openproblems are discussed.