Bernd Hofmann et al 2009 Inverse Problems 25 115013 doi:10.1088/0266-5611/25/11/115013
Bernd Hofmann1, Peter Mathé2 and Heinrich von Weizsäcker3
Show affiliationsThe authors study ill-posed equations with unbounded operators in Hilbert space. This setup has important applications, but only a few theoretical studies are available. First, the question is addressed and answered whether every element satisfies some general source condition with respect to a given self-adjoint unbounded operator. This generalizes a previous result from Mathé and Hofmann (2008 Inverse Problems 24 015009). The analysis then proceeds to error bounds for regularization, emphasizing some specific points for regularization under unbounded operators. The study finally reviews two examples within the light of the present study, as these are fractional differentiation and some Cauchy problems for the Helmholtz equation, both studied previously and in more detail by U Tautenhahn and co-authors.
Issue 11 (November 2009)
Received 1 July 2009, in final form 22 September 2009
Published 29 October 2009
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