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On multiplication operators occurring in inverse problems of natural sciences and stochastic finance

We deal with locally ill-posed nonlinear operator equations F(x) = y in L^2(0,1),
where the Fréchet derivatives A = F'(x_0) of the nonlinear forward operator F are
compact linear integral operators A = M ◦ J with a multiplication operator M
with integrable multiplier function m and with the simple integration operator J.
In particular, we give examples of nonlinear inverse problems in natural sciences
and stochastic finance that can be written in such a form with linearizations that
contain multiplication operators. Moreover, we consider the corresponding ill-posed
linear operator equations Ax = y and their degree of ill-posedness. In particular,
we discuss the fact that the noncompact multiplication operator M has only a
restricted influence on this degree of ill-posedness even if m has essential zeros of
various order.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18375
Date07 October 2005
CreatorsHofmann, Bernd
PublisherTechnische Universität Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:lecture, info:eu-repo/semantics/lecture, doc-type:Text
Rightsinfo:eu-repo/semantics/openAccess
Relationurn:nbn:de:swb:ch1-200501214, qucosa:18370

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