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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
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 $J_1$ and $J^\prime_1$. The correct operator involves all endomorphisms, $J_\alpha$, 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$\times$ball- and sphere$\times$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 $\sigma$ deformations.