5 citations · 18 across the 7 of their papers we have counts for
7 papers · 1 filter
Level sets of the resolvent norm of a linear operator revisited
E. B. Davies, Eugene Shargorodsky
It is proved that the resolvent norm of an operator with a compact resolvent on a Banach space cannot be constant on an open set if the underlying space or its dual is complex…
Sectorial perturbations of self-adjoint matrices and operators
E. B. Davies
This paper considers matrices of the form , where is self-adjoint, and is a non-self-adjoint perturbation of . We obtain some monodromy-t…
Singular Schrodinger operators in one dimension
E. B. Davies
We consider a class of singular Schrödinger operators that act in , each of which is constructed from a positive function on . Our analysis is di…
Convergence of eigenvalues for a highly non-self-adjoint differential operator
E. B. Davies, John Weir
In this paper we study a family of operators dependent on a small parameter , which arise in a problem in fluid mechanics. We show that the spectra of these operators converg…
Spectral Properties of Matrices Associated with Some Directed Graphs
E. B. Davies, Paul A. Incani
We study the spectral properties of certain non-self-adjoint matrices associated with large directed graphs. Asymptotically the eigenvalues converge to certain curves, apart from a…
Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle
E. B. Davies, Barry Simon
We prove that for any matrix, , and with , we have that $\|(z-A)^{-1}\|\leq\cot (\fracπ{4n}) \dist (z, \spec(A))^{-1}$. We apply this result to th…