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Published June 2000 | public
Journal Article

Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum

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 Schrödinger operator H = -(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.

Additional Information

© Copyright 2000 by the Authors. Received by the editors October 9, 1997. This material is based upon work supported by the National Science Foundation under Grant Nos. DMS-9623121 and DMS-9401491.

Additional details

Created:
August 19, 2023
Modified:
October 18, 2023