87 citations · 126 across the 14 of their papers we have counts for
15 papers
The spectral form of the functional model for maximally dissipative operators: A Lagrange identity approach
B. Malcolm Brown, Marco Marletta, Sergey Naboko +1
The spectral and scattering properties of non-selfadjoint problems pose a mathematical challenge. Apart from exceptional cases, the well-developed methods used to examine the spect…
Spectrum of the Maxwell Equations for a Flat Interface between Homogeneous Dispersive Media
Malcolm Brown, Tomáš Dohnal, Michael Plum +1
The paper determines and classifies the spectrum of a non-self-adjoint operator pencil generated by the time-harmonic Maxwell problem with a nonlinear dependence on the frequency f…
Complete Non-Selfadjointness for Schrödinger Operators on the Semi-Axis
Christoph Fischbacher, Serguei Naboko, Ian Wood
In this note we investigate complete non-selfadjointness for all maximally dissipative extensions of a Schrödinger operator on a half-line with dissipative bounded potential and di…
The inverse problem for a spectral asymmetry function of the Schrödinger operator on a finite interval
B. Malcolm Brown, Karl Michael Schmidt, Stephen P. Shipman +1
For the Schrödinger equation on a finite -interval, there is defined an "asymmetry function" , which is entire of order and type in…
Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach
Edmund Judge, Sergey Naboko, Ian Wood
We consider the problem of embedding eigenvalues into the essential spectrum of periodic Jacobi operators, using an oscillating, decreasing potential. To do this we employ a geomet…
Essential spectrum for Maxwell's equations
Giovanni S. Alberti, Malcolm Brown, Marco Marletta +1
We study the essential spectrum of operator pencils associated with anisotropic Maxwell equations, with permittivity , permeability and conductivity , on finite…
Weyl Solutions and J-selfadjointness for Dirac operators
B. Malcolm Brown, Martin Klaus, Mark Malamud +2
We consider a non-selfadjoint Dirac-type differential expression \begin{equation} D(Q)y:= J_n \frac{dy}{dx} + Q(x)y, \quad\quad\quad (1) \end{equation} with a non-selfadjoint poten…
Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique
Edmund Judge, Sergey Naboko, Ian Wood
For an arbitrary Hermitian period- Jacobi operator, we assume a perturbation by a Wigner-von Neumann type potential to devise subordinate solutions to the formal spectral equati…
The Proper Dissipative Extensions of a Dual Pair
Christoph Fischbacher, Sergey Naboko, Ian Wood
Let and be dissipative operators on a Hilbert space and let form a dual pair, i.e. , resp.\ $\wide…
Eigenvalues for perturbed periodic Jacobi matrices by the Wigner-von Neumann approach
Edmund Judge, Sergey Naboko, Ian Wood
The Wigner-von Neumann method, which was previously used for perturbing continuous Schrödinger operators, is here applied to their discrete counterparts. In particular, we consider…
Gap localization of TE-Modes by arbitrarily weak defects
Malcolm Brown, Vu Hoang, Michael Plum +2
This paper considers the propagation of TE-modes in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic background medium. Both the…
Some spectral properties of Rooms and Passages domains and their skeletons
B. M. Brown, W. D. Evans, I. G. Wood
In this paper we investigate spectral properties of Lapla- cians on Rooms and Passages domains. In the first part, we use Dirichlet- Neumann bracketing techniques to show that for…
Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems
Helmut Abels, Gerd Grubb, Ian Geoffrey Wood
For a strongly elliptic second-order operator on a bounded domain it has been known for many years how to interpret the general closed -realizat…
The abstract Titchmarsh-Weyl M-function for adjoint operator pairs and its relation to the spectrum
Malcolm Brown, James Hinchcliffe, Marco Marletta +2
In the setting of adjoint pairs of operators we consider the question: to what extent does the Weyl M-function see the same singularities as the resolvent of a certain restriction…
Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices
Malcolm Brown, Marco Marletta, Serguei Naboko +1
Starting with an adjoint pair of operators, under suitable abstract versions of standard PDE hypotheses, we consider the Weyl M-function of extensions of the operators. The extensi…