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Microlocal analysis of scattering data for nested conormal potentials

Eswarathasan, Suresh 2012. Microlocal analysis of scattering data for nested conormal potentials. Journal of Functional Analysis 262 (5) , pp. 2100-2141. 10.1016/j.jfa.2011.12.013

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Working in the time domain, we show that the location of the singularities and the principal symbol of a potential that is conormal to nested submanifolds S2⊂S1⊂Rn, for n⩾3, can be recovered from the backscattering as well as from the restriction of the far-field pattern to more general determined sets of scattering data. This extends the work of Greenleaf and Uhlmann where the potentials considered are conormal to a single submanifold S⊂Rn. We utilize the microlocal analysis of the wave operator and multiplication by a nested conormal distribution in order to study their action on spaces of conormal-like distributions.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Elsevier
ISSN: 0022-1236
Date of Acceptance: 12 December 2011
Last Modified: 01 Feb 2020 03:19

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