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math.SP2025
Cycle intersection form and oscillation of graph eigenfunctions
Gregory Berkolaiko, Jared C. Bronski, Mark Goresky
For a real symmetric matrix strictly supported on a finite simple graph, it is shown that the inertia of a weighted intersection form on the cycle space of the graph, with weig…
math.SP2024
The calculus of Duistermaat's triple index
Gregory Berkolaiko, Graham Cox, Yuri Latushkin +1
In this paper we develop a systematic calculus for the Duistermaat index, a symplectic invariant defined for triples of Lagrangian subspaces. Introduced nearly half a century ago,…
math.SP2023
The Duistermaat index and eigenvalue interlacing for self-adjoint extensions of a symmetric operator
Gregory Berkolaiko, Graham Cox, Yuri Latushkin +1
Eigenvalue interlacing is a useful tool in linear algebra and spectral analysis. In its simplest form, the interlacing inequality states that a rank-one positive perturbation shift…