97-130 Gesztesy F., Simon B.
Inverse Spectral Analysis With Partial Information on the Potential, II. The Case of Discrete Spectrum (67K, AMS-TeX) Mar 17, 97
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Abstract. We discuss results where the discrete spectrum (or partial information on the discrete spectrum) and partial information on the potential $q$ of a one-dimensional Schr\"odinger 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, we 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.

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