

Preprint 19/2008
Reconstruction of the intertwining operator and new striking examples added to "Isospectral pairs of metrics on balls and spheres with different local geometries"
Zoltan I. Szabo
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Submission date: 13. Feb. 2008
Pages: 45
Bibtex
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Abstract:
The intertwining operator constructed in Annals of Mathematics, 154(2001), 437-475;
and 161(2005), 343-395 does not appear in the right form. It is established there by
using only the
anticommutators and
. The correct operator
involves all endomorphisms,
, which are unified
by the Z-Fourier transform.
Although some of the correct elements of the
previous constructions are kept, this idea is
established by a new technique
which yields the various
isospectrality theorems stated in the papers
on a much larger scale.
The new results include
new isospectrality examples living on sphere
ball-
and sphere
sphere-type manifolds. Among them, there are such
discrete isospectrality families where one of the members is
homogeneous while the others are locally inhomogeneous (striking examples).
Furthermore, a large class of new isospectrality families are constructed
by
deformations.