Spectral flow for pair compatible equipartitions

We show that a recent spectral flow approach proposed by Berkolaiko-Cox-Marzuola for analyzing the nodal deficiency of the nodal partition associated to an eigenfunction can be extended to more general partitions. To be more precise, we work with spectral equipartitions that satisfy a pair compatibl...

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Bibliographic Details
Published inCommunications in partial differential equations Vol. 47; no. 1; pp. 169 - 196
Main Authors Helffer, Bernard, Sundqvist, Mikael Persson
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 2022
Taylor & Francis Ltd
Subjects
Aharonov-Bohm Hamiltonians
Dirichlet problem
Dirichlet-to-Neumann operators
Eigenvectors
Matematik
Matematisk analys
Mathematical Analysis
Mathematics
Natural Sciences
Naturvetenskap
nodal deficiency
Operators
Slitting
Spectra
Spectral flow
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Summary:We show that a recent spectral flow approach proposed by Berkolaiko-Cox-Marzuola for analyzing the nodal deficiency of the nodal partition associated to an eigenfunction can be extended to more general partitions. To be more precise, we work with spectral equipartitions that satisfy a pair compatible condition. Nodal partitions and spectral minimal partitions are examples of such partitions. Along the way, we discuss different approaches to the Dirichlet-to-Neumann operators: via Aharonov-Bohm operators, via a double covering argument, and via a slitting of the domain.
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2021.1955257