The Inverse Resonance Problem for Hermite Operators

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