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Krein’s inverse spectral theorem describes the spectral measures τ of the differential operators DmDx with boundary condition f_′(0)=0, if m runs through all nondecreasing functions on [0, ∞). This result will be extended to boundary conditions of the type af_′(0)−f(0)=0 (a ε [0, ∞)).  Other conditions as in Krein’s theorem appear.

An extension of Krein’s inverse spectral theorem to strings with nonreflecting left boundaries