Gesztesy F., Simon B.
Inverse Spectral Analysis With Partial Information on the
Potential, II. The Case of Discrete Spectrum
(67K, AMS-TeX)
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.