Recovery of the Potential from I-Function

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dc.contributor.author Ramm, Alexander G.
dc.date.accessioned 2015-07-13T18:57:29Z
dc.date.available 2015-07-13T18:57:29Z
dc.identifier.uri http://hdl.handle.net/2097/19778
dc.description.abstract The inverse scattering problem on half-axis, in other words, in the spherically symmetric case, consists of finding the unknown potential from a suitable class from the scattering data S. The other problem of practical interest is to find this potential from the spectral data dp(λ). In the literature there are recovery procedures for finding the potential from the spectral or from the scattering data. Define the I-function: I(k) := f'(0,k)/f(k) , where f(x,k) is the Jost solution. Constructive ways to find I(k) from dp(λ) and vice versa, and I(k) from S and vice versa are given. The theory of Riemann problem is used as an essential tool. If I(k) is found, then our methods allow one to construct the scattering data and from these recover the potential by the known procedure. Alternatively, one can construct from I(k) the spectral data and from these find the potential by the known procedure. MSC: 34A55 en_US
dc.language.iso en_US en_US
dc.publisher Elsevier en_US
dc.relation.uri http://www.sciencedirect.com/science/article/pii/S0034487714000202 en_US
dc.rights doi:10.1016/S0034-4877(14)00020-2. Released under CC BY-NC-ND 4.0, https://creativecommons.org/licenses/by-nc-nd/4.0/. Sherpa/RoMEO record can be found at: http://www.sherpa.ac.uk/romeo/issn/0034-4877/. en_US
dc.subject I-function; Riemann problem; Scattering data; Spectral data; Inverse problem en_US
dc.title Recovery of the Potential from I-Function en_US
dc.type Article (author version) en_US
dc.date.published 2014 en_US
dc.citation.doi 10.1016/S0034-4877(14)00020-2 en_US
dc.citation.epage 143 en_US
dc.citation.issn 0034-4877 en_US
dc.citation.issue 2 en_US
dc.citation.jtitle Reports on Mathematical Physics en_US
dc.citation.spage 135 en_US
dc.citation.volume 74 en_US
dc.contributor.authoreid ramm en_US


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