49 citations · 289 across the 45 of their papers we have counts for
20 papers · 1 filter
The pseudospectrum of an operator with Bessel-type singularities
Lyonell Boulton, Marco Marletta
In this paper we examine the asymptotic structure of the pseudospectrum of the singular Sturm-Liouville operator subject to periodic boundary…
Completeness of trajectories associated to Appell hypergeometric functions
Lyonell Boulton
We examine the linear completeness of trajectories of eigenfunctions associated to non-linear eigenvalue problems, subject to Dirichlet boundary conditions on a segment. We pursue…
Perturbations of Gibbs semigroups and the non-selfadjoint harmonic oscillator
Lyonell Boulton
Let be the generator of a -semigroup which is of finite trace for all (a Gibbs semigroup). Let be another closed operator, -bounded with -bound e…
On the quality of complementary bounds for eigenvalues
L. Boulton, A. Hobiny
A concrete formulation of the Lehmann-Maehly-Goerisch method for semi-definite self-adjoint operators with compact resolvent is considered. Precise rates of convergence are determi…
On the stability of a forward-backward heat equation
Lyonell Boulton, Marco Marletta, David Rule
In this paper we examine spectral properties of a family of periodic singular Sturm-Liouville problems which are highly non-self-adjoint but have purely real spectrum. The problem…
Eigenvalue enclosures and convergence for the linearized MHD operator
Lyonell Boulton, Michael Strauss
We discuss how to compute certified enclosures for the eigenvalues of benchmark linear magnetohydrodynamics operators in the plane slab and cylindrical pinch configurations. For th…
Generalised Weyl theorems and spectral pollution in the Galerkin method
Lyonell Boulton, Nabile Boussaid, Mathieu Lewin
We consider a general framework for investigating spectral pollution in the Galerkin method. We show how this phenomenon is characterised via the existence of particular Weyl seque…
Approximation properties of the -sine bases
Lyonell Boulton, Gabriel Lord
For the eigenfunctions of the non-linear eigenvalue problem associated to the one-dimensional -Laplacian are known to form a Riesz basis of . We examine in t…
On the convergence of second order spectra and multiplicity
Lyonell Boulton, Michael Strauss
Let A be a self-adjoint operator acting on a Hilbert space. The notion of second order spectrum of A relative to a given finite-dimensional subspace L has been studied recently in…
On a class of non-self-adjoint periodic boundary value problems with discrete real spectrum
Lyonell Boulton, Michael Levitin, Marco Marletta
In [arXiv:0801.0172] we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenva…
On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities
Lyonell Boulton, Michael Levitin, Marco Marletta
We prove that the spectrum of a certain PT-symmetric periodic problem is purely real. Our results extend to a larger class of potentials those recently found by Brian Davies [math.…
On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators
Lyonell Boulton, Michael Levitin
This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrodinger operator perturbed by a fast decreasing potentia…
On the boundary of the pseudospectrum and its fault points
Lyonell Boulton, Peter Lancaster
The theme of this paper was motivated by the question: How effective are path-following procedures for tracing the pseudospectral boundary? The present study of the mathematical pr…
Stability of Quadratic Projection Methods
Lyonell Boulton, Michael Strauss
In this paper we discuss the stability of an alternative pollution-free procedure for computing spectra. The main difference with the Galerkin method lies in the fact that it gives…
On Pseudospectra of Matrix Polynomials and their Boundaries
Lyonell Boulton, Peter Lancaster, Panayiotis Psarrakos
In the first part of this paper, the main concern is with smoothness properties of the boundary of the pseudospectrum of a matrix polynomial. In the second part, results are obtain…
Non-variational approximation of discrete eigenvalues of self-adjoint operators
Lyonell Boulton
We establish sufficiency conditions in order to achieve approximation to discrete eigenvalues of self-adjoint operators in the second-order projection method suggested recently by…
Limiting set of second order spectra
Lyonell Boulton
M.Levitin and E.Shargorodsky purposed in a recent article, [math.SP/0212087], the use of the so called ``second order relative spectrum'', to find eigenvalues of self-adjoint opera…
Projection methods for discrete Schrodinger operators
Lyonell S. Boulton
Let be the discrete Schrödinger operator , acting on where the potential is real-valued and as $n\to \i…
Spectral behaviour of a simple non-self-adjoint operator
L. S. Boulton
We investigate the spectrum of a typical non-self-adjoint differential operator acting on $\Lp(0,1)\otimes \mathbb{C}^2$, where is a constan…
Non-self-adjoint harmonic oscillator, compact semigroups and pseudospectra
Lyonell S. Boulton
We provide new information concerning the pseudospectra of the complex harmonic oscillator. Our analysis illustrates two different techniques for getting resolvent norm estimates.…