Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum |
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Authors: | Fritz Gesztesy Barry Simon |
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Affiliation: | Department of Mathematics, University of Missouri, Columbia, Missouri 65211 ; Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125 |
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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 of a one-dimensional Schrödinger operator 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 on a finite interval and knowledge of over a corresponding fraction of the interval. The methods employed rest on Weyl -function techniques and densities of zeros of a class of entire functions. |
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