caa a22 4500 378866559 CHVBK 20180305123359.0 cr unu---uuuuu 161128e20030901xx s 000 0 eng 10.1515/156939403769237015 doi (NATIONALLICENCE)gruyter-10.1515/156939403769237015 Arens T. Mathematisches Institut II, Universität Karlsruhe, 76128 Karlsruhe, Germany. E-mail: arens@numathics.com An approximation property of elastic Herglotz wave functions and its application in the linear sampling method [Elektronische Daten] [T. Arens] Herglotz wave functions play an important role in a class of reconstruction methods for inverse scattering problems known as linear sampling methods. We here consider these functions in the setting of linearized elasticity and derive representations in terms of eigenfunctions to the Navier operator in two spatial dimensions. We then show the important property that the elastic Herglotz Wave functions are dense in the space of solutions to the Navier equation with respect to the [H 1 (D)]2 norm for any bounded Lipschitz domain D. The proof of this property in three-dimensions, not essentially different from the 2D argument, is also outlined. The paper is concluded with an application of the approximation property in the mathematical foundation of the linear sampling method for the reconstruction of rigid obstacles from the knowledge of the far field operator. Copyright 2003, Walter de Gruyter Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/3(2003-09-01), 219-233 0928-0219 11:3<219 2003 11 jiip https://doi.org/10.1515/156939403769237015 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939403769237015 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Arens T. Mathematisches Institut II, Universität Karlsruhe, 76128 Karlsruhe, Germany. E-mail: arens@numathics.com NATIONALLICENCE 773 0- Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/3(2003-09-01), 219-233 0928-0219 11:3<219 2003 11 jiip CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter