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The Inverse Resonance Problem for Hermite Operators

Authors:	B Malcolm Brown Serguei Naboko Rudi Weikard

Institution:	(1) Department of Computer Science, Cardiff University, Cardiff, CF2 3XF, UK;(2) Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294-1170, USA

Abstract:	In this paper the inverse resonance problem for the Hermite operator is investigated. The Hermite operator $H=\mathfrak{a}+\mathfrak{a}^{}+b$ with the creation operator $\mathfrak{a}$ , the annihilation operator $\mathfrak{a}^{}$ , 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.

Keywords:	Inverse problems Eigenvalues and resonances Hermite operator Perturbation determinant
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