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# The Inverse Resonance Problem for Hermite Operators

 Brown, Brian Malcolm, Naboko, Serguei and Weikard, Rudi 2009. The Inverse Resonance Problem for Hermite Operators. Constructive Approximation 30 (2) , pp. 155-174. 10.1007/s00365-008-9037-8

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## Abstract

In this paper the inverse resonance problem for the Hermite operator is investigated. The Hermite operator H=\mathfraka+\mathfraka*+bUnknown control sequence '\mathfrak' with the creation operator \mathfrakaUnknown control sequence '\mathfrak' , the annihilation operator \mathfraka*Unknown control sequence '\mathfrak' , and a finitely supported multiplication operator b, is an unbounded operator on ℓ 2(ℕ0) having finitely many eigenvalues and infinitely many resonances (except for b=0, when there are no eigenvalues or resonances). It is shown that knowing the location of eigenvalues and resonances determines the potential b uniquely.

Item Type: Article Publication Published Computer Science & Informatics Q Science > QA Mathematics > QA75 Electronic computers. Computer science Inverse problems - Eigenvalues and resonances - Hermite operator - Perturbation determinant Springer 0176-4276 04 Jun 2017 02:53 http://orca-mwe.cf.ac.uk/id/eprint/13393