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Inverse spectral analysis with partial information on the potential. II: The case of discrete spectrum. (English) Zbl 0948.34060
The authors discuss results where the discrete spectrum (or partial information on the discrete spectrum) and partial information on the potential $q$ of a one-dimensional Schrödinger operator $H=-\frac{d^{2}}{dx^{2}}+q$ determine the potential completely. Included are theorems for finite intervals and for the whole line. In particular, the authors pose and solve a new type of inverse spectral problem involving fractions of the eigenvalues of $H$ on a finite interval and knowledge of $q$ over a corresponding fraction of the interval. The methods employed rest on Weyl $m$-function techniques and densities of zeros of a class of entire functions. For part I see [Helv. Phys. Acta 70, No. 1-2, 66-71 (1997; Zbl 0870.34017)].

34L40Particular ordinary differential operators
34A55Inverse problems of ODE
34B20Weyl theory and its generalizations
34B24Sturm-Liouville theory
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