Computing nodal deficiency with a refined spectral flow (after G. Berkolaiko, G. Cox, B. Helffer, and M. Persson Sundqvist

Bernard Helffer (U of Nantes)

Nov 11. 2022, 14:00 — 14:45

Recent work of the authors and their collaborators has uncovered fundamental connections between the Dirichlet-to-Neumann map, the spectral flow of a certain family of self-adjoint operators, and the nodal deficiency of a Laplacian eigenfunction (or an analogous deficiency associated to a non-bipartite equipartition). Using a more refined construction of the Dirichlet-to-Neumann map, we strengthen all of these results, in particular getting improved bounds on the nodal deficiency of degenerate eigenfunctions. Our framework is very general, allowing for non-bipartite partitions, non-simple eigenvalues, and non-smooth nodal sets. Consequently, our results can be used in the general study of spectral minimal partitions, not just nodal partitions of generic Laplacian eigenfunctions.
 


 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Spectral Theory of Differential Operators in Quantum Theory (Workshop)
Organizer(s):
Jussi Behrndt (TU Graz)
Fritz Gesztesy (Baylor U, Waco)
Ari Laptev (Imperial College London)
Christiane Tretter (U Bern)