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
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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 sphereball- and spheresphere-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.