9 citations · 13 across the 6 of their papers we have counts for
10 papers · 1 filter
Triviality of the Peripheral Point Spectrum
E. B. Davies
If $T_t=\rme^{Zt}$ is a positive one-parameter contraction semigroup acting on where is a countable set and , then the peripheral point spectrum o…
Semi-classical Analysis and Pseudospectra
E. B. Davies
We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second order differential operators in the semi-classical limit. This le…
Asymptotic behaviour of quasi-orthogonal polynomials
E. B. Davies
We obtain explicit upper and lower bounds on the norms of the spectral projections of the non-self-adjoint harmonic oscillator. Some of our results apply to a variety of other fami…
Approximating semigroups by using pseudospectra
E. B. Davies
We study evolution equations with non-self-adjoint generators, for example the convection-diffusion equation. Spectral expansions are not a reliable method of solving such equation…
Spectral Pollution
E B Davies, M Plum
We discuss the problems arising when computing eigenvalues of self-adjoint operators which lie in a gap between two parts of the essential spectrum. Spectral pollution, i.e. the ap…
Semigroup Growth Bounds
E B Davies
We prove lower bounds on , where is a one-parameter semigroup, starting from information on the resolvent norms, i.e. the pseudospectra. We provide a physically impo…