92 citations · 184 across the 24 of their papers we have counts for
25 papers
Spectra of a class of non-self-adjoint matrices
E. Brian Davies, Michael Levitin
We consider a new class of non-self-adjoint matrices that arise from an indefinite self-adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the…
Spectrum of a Feinberg-Zee Random Hopping Matrix
Simon N Chandler-Wilde, E Brian Davies
This paper provides a new proof of a theorem of Chandler-Wilde, Chonchaiya and Lindner that the spectra of a certain class of infinite, random, tridiagonal matrices contain the uni…
C*-algebras associated with some second order differential operators
E Brian Davies, Vladimir Georgescu
We compare two C*-algebras that have been used to study the essential spectrum. This is done by considering a simple second order elliptic differential operator acting in L^2(R^N),…
An Inverse Spectral Theorem
E. B. Davies
We prove a substantial extension of an inverse spectral theorem of Ambarzumyan, and show that it can be applied to arbitrary compact Riemannian manifolds, compact quantum graphs an…
Algebraic aspects of spectral theory
E. B. Davies
We describe some aspects of spectral theory that involve algebraic considerations but need no analysis. Some of the important applications of the results are to the algebra of $n\t…
Non-Weyl asymptotics for quantum graphs with general coupling conditions
E. Brian Davies, Pavel Exner, Jiri Lipovsky
Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for t…