Trace and Regularized Index of Callias Operators on Hyperbolic SpaceOberseminar Global Analysis and Operator Algebras

by Jilly Kevo (University of Bonn)

Tuesday Feb 3, 2026, 2:15 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60/1-008 (Mathezentrum)

We consider non-Fredholm Callias operators $D$ on odd-dimensional hyperbolic space, that is, hyperbolic Dirac operators perturbed by operator-valued potentials without any assumption of uniform invertibility at infinity. In this non-Fredholm setting, the classical Fredholm index is replaced by the Witten index, defined through trace limits of the associated heat semigroups.

Building on the framework developed in the first talk, we derive an explicit formula for the iterated trace of the difference of heat semigroups associated with $D^*D$  and $DD^*$. Our approach combines Fourier-Helgason analytic methods on symmetric spaces with Volterra-type constructions of heat kernels, adapted to the curved setting of hyperbolic space.

Earlier results in one dimension, firstly published by Pushnitski, and later generalized by Gesztesy et al. and Carey et al. were extended to Euclidean odd-dimensional space by Fürst.

The result presented in this talk constitutes the first explicit trace formula of this type in a multi-dimensional, non-Euclidean setting.