The interior transmission eigenvalue problem

Cakoni, F; Colton, D; Gintides, D

dc.contributor.author	Cakoni, F	en
dc.contributor.author	Colton, D	en
dc.contributor.author	Gintides, D	en
dc.date.accessioned	2014-03-01T01:34:46Z
dc.date.available	2014-03-01T01:34:46Z
dc.date.issued	2010	en
dc.identifier.issn	0036-1410	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20845
dc.subject	Inhomogeneous medium	en
dc.subject	Interior transmission problem	en
dc.subject	Inverse scattering	en
dc.subject	Transmission eigenvalues	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Complex eigenvalues	en
dc.subject.other	Complex planes	en
dc.subject.other	Eigen-value	en
dc.subject.other	Eigenvalue problem	en
dc.subject.other	Eigenvalues	en
dc.subject.other	Field patterns	en
dc.subject.other	Homogeneous media	en
dc.subject.other	Index of refraction	en
dc.subject.other	Inhomogeneous medium	en
dc.subject.other	Interior transmission problems	en
dc.subject.other	Inverse scattering	en
dc.subject.other	Scattered waves	en
dc.subject.other	Inverse problems	en
dc.subject.other	Refraction	en
dc.subject.other	Refractive index	en
dc.subject.other	Scattering	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.title	The interior transmission eigenvalue problem	en
heal.type	journalArticle	en
heal.identifier.primary	10.1137/100793542	en
heal.identifier.secondary	http://dx.doi.org/10.1137/100793542	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	We consider the inverse problem of determining the spherically symmetric index of refraction n(r) from a knowledge of the corresponding transmission eigenvalues (which can be determined from field pattern of the scattered wave). We also show that for constant index of refraction n(r) = n, the smallest transmission eigenvalue suffices to determine n, complex eigenvalues exist for n sufficiently small and, for homogeneous media of general shape, determine a region in the complex plane where complex eigenvalues must lie. © 2010 Society for Industrial and Applied Mathematics.	en
heal.publisher	SIAM PUBLICATIONS	en
heal.journalName	SIAM Journal on Mathematical Analysis	en
dc.identifier.doi	10.1137/100793542	en
dc.identifier.isi	ISI:000285508100022	en
dc.identifier.volume	42	en
dc.identifier.issue	6	en
dc.identifier.spage	2912	en
dc.identifier.epage	2921	en