256 citations · 944 across the 58 of their papers we have counts for
65 papers
On a conjectured property of the Witten index and an application to Levinson's theorem
Alan Carey, Galina Levitina
A few years ago Fritz Gesztesy raised the issue of whether there was a composition rule for the Witten index analogous to that satisfied by Fredholm operators. In this note we prov…
The limiting absorption principle for massless Dirac operators, properties of spectral shift functions, and an application to the Witten index of non-Fredholm operators
Alan Carey, Fritz Gesztesy, Galina Levitina +3
We derive a limiting absorption principle on any compact interval in for the free massless Dirac operator, in $[L^2(\mathbb…
The Witten index and the spectral shift function
Alan Carey, Galina Levitina, Denis Potapov +1
In \cite{APSIII} Atiyah, Patodi and Singer introduced spectral flow for elliptic operators on odd dimensional compact manifolds. They argued that it could be computed from the Fred…
The Fermi gerbe of Weyl semimetals
Alan Carey, Guo Chuan Thiang
In the gap topology, the unbounded self-adjoint Fredholm operators on a Hilbert space have third homotopy group the integers. We realise the generator explicitly, using a family of…
The product formula for regularized Fredholm determinants
Thomas Britz, Alan Carey, Fritz Gesztesy +3
For trace class operators ( a complex, separable Hilbert space), the product formula for Fredholm determinants holds in the famil…
The KO-valued spectral flow for skew-adjoint Fredholm operators
Chris Bourne, Alan L. Carey, Matthias Lesch +1
In this article we give a comprehensive treatment of a `Clifford module flow' along paths in the skew-adjoint Fredholm operators on a real Hilbert space that takes values in KO${}_…