UNIQUENESS THEOREMS IN INVERSE SPECTRAL THEORY

CHRISTER BENNEWITZ

christer.bennewitz@math.lu.se

Department of Mathematics

Lund University

Box 118

SE-22100 Lund, Sweden

Lund University

Box 118

SE-22100 Lund, Sweden

The celebrated Borg-Marchenko uniqueness theorem says that given
the spectral measure of a selfadjoint operator generated by a
Sturm-Liouville operator
, then the potential
is determined. I will review this result and then discuss
uniqueness theorems of the same nature, but for more general
situations. I will discuss matrix-valued equations, higher order
equations, the general Sturm-Liouville equation
and so called left-definite
Sturm-Liouville equations. For some of these results method
similar to those originally employed by Borg may be used, but some
results depend on a new approach, using a generalized version of
the classical Paley-Wiener theorem for the Fourier transform.

EPSRC Gregynog Workshop, 21-26 July 2002