Group Seminar: Transfer Group (TG)
Time: April 24, 2024, 14:00
Room: RICAM, SP2, 416-2
In this talk, we present new results on the degree and on the interval of ill-posedness from a series of
recently published studies. We distinguish ill-posedness of type I and type II in the sense of Nashed
for linear inverse problems in Hilbert spaces with compact and non-compact forward operators. Since
only for compact operators the strength of ill-posedness can be simply characterized by decay rates of
singular values, we also discuss concepts for handling the non-compact case. In particular, the potential
of noncompact operators in compositions with compact ones for changing the ill-posedness degree is of
interest. The Hausdorff moment operator and the Ces`aro operator as non-compact examples provide
considerable insights in combination with compact integration operators. Moreover, the specifics of
singular value decay rates of compact operators in higher dimensions is under consideration by using the
multivariate integration operator, which occurs for example in copula density reconstruction.
The talk partially presents results of joint work with Stefan Kindermann (Linz), FrankWerner (W¨urzburg),
Robert Plato (Siegen) Hans-J¨urgen Fischer (Dresden), Peter Math´e (Berlin) and Yu Deng (Chemnitz).
Research is supported by the Deutsche Forschungsgemeinschaft (DFG) under grant HO 1454/13-1.