caa a22 4500 467932174 CHVBK 20180406152946.0 cr unu---uuuuu 170328e20060301xx s 000 0 eng 10.1007/s00020-004-1355-z doi (NATIONALLICENCE)springer-10.1007/s00020-004-1355-z Grinberg N. Mathematisches Institut II, Universität Karlsruhe (TH), D-76128, Karlsruhe, Germany aut The Operator Factorization Method in Inverse Obstacle Scattering [Elektronische Daten] [N. Grinberg] Abstract.: The standard factorization method from inverse scattering theory allows to reconstruct an obstacle pointwise from the normal far field operator F. The kernel of this method is the study of the first kind Fredholm integral equation (F*F)1/4f=Φz with the right-hand part $$\Phi _{z} {\left( \theta \right)} = \exp {\left( { - ikz \cdot \theta } \right)}.$$ In this paper we extend the factorization method to cover some kinds of boundary conditions which leads to non-normal far field operators. We visualize the scatterer explicitly in terms of the singular system of the selfadjoint positive operator F#=[(ReF)* (ReF)]1/2+ImF. The following characterization criterium holds: a given point z is inside the obstacle if and only if the function Φz belongs to the range of F#1/2. Our operator approach provides the tool for treatment of a wide class of inverse elliptic problems. Birkhäuser Verlag, Basel, 2006 Helmholtz operator nationallicence far field operator nationallicence inverse obstacle scattering problem nationallicence factorization method nationallicence Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/3(2006-03-01), 333-348 0378-620X 54:3<333 2006 54 20 https://doi.org/10.1007/s00020-004-1355-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-004-1355-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Grinberg N. Mathematisches Institut II, Universität Karlsruhe (TH), D-76128, Karlsruhe, Germany aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/3(2006-03-01), 333-348 0378-620X 54:3<333 2006 54 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer