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Bitte nutzen Sie beim Zitieren immer folgende Url:

http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501261

Kurzfassung in Englisch

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.

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