200 citations · 1k across the 51 of their papers we have counts for
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Spectral shift via "lateral" perturbation
G. Berkolaiko, P. Kuchment
We consider a compact perturbation of a self-adjoint operator with an eigenvalue below its essential spectrum and the corresponding eigenfunctio…
Liouville-Riemann-Roch theorems on abelian coverings
Minh Kha, Peter Kuchment
The classical Riemann-Roch theorem has been extended by N. Nadirashvili and then M. Gromov and M. Shubin to computing indices of elliptic operators on compact (as well as non-compa…
Index theorems for quantum graphs
S. A. Fulling, P. Kuchment, J. H. Wilson
In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle conc…
Coincidence of length spectra does not imply isospectrality
S. A. Fulling, Peter Kuchment
Penrose--Lifshits mushrooms are planar domains coming in nonisometric pairs with the same geodesic length spectrum. Recently S. Zelditch raised the question whether such billiards…