Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS 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

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 $J_1$ 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.

Received:
Jan 17, 2008
Published:
Jan 17, 2008

Related publications

Preprint
2008 Repository Open Access
Zoltán Szabó

Reconstruction of the intertwining operator and new striking examples added to 'Isospectral pairs of metrics on balls and spheres with different local geometries'