Rayleigh estimates for differential operators on graphs | Zendy

Pavel Kurasov | Zendy; Serguei Naboko | Zendy

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Rayleigh estimates for differential operators on graphs

Author(s) -

Pavel Kurasov,

Serguei Naboko

Publication year - 2014

Publication title -

journal of spectral theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.063

H-Index - 19

eISSN - 1664-0403

pISSN - 1664-039X

DOI - 10.4171/jst/67

Subject(s) - mathematics , spectral gap , eigenvalues and eigenvectors , uniqueness , differential operator , laplace transform , graph , metric (unit) , spectral geometry , interval (graph theory) , spectral theorem , spectral properties , mathematical analysis , pure mathematics , operator theory , discrete mathematics , combinatorics , physics , quantum mechanics , operations management , astrophysics , economics

We study the spectral gap, i.e. the distance between the two lowest eigenvalues for Laplace operators on metric graphs. A universal lower estimate for the spectral gap is proven and it is shown that it is attained if the graph is formed by just one interval. Uniqueness of the minimizer allows to prove a geometric version of the Ambartsumian theorem derived originally for Schrodinger operators.

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