Zobrazeno 1 - 10
of 337
pro vyhledávání: '"Brown, B. M."'
Publikováno v:
Integral Equations and Operator Theory 2019
This paper discusses how much information on a Friedrichs model operator can be detected from `measurements on the boundary'. We use the framework of boundary triples to introduce the generalised Titchmarsh-Weyl $M$-function and the detectable subspa
Externí odkaz:
http://arxiv.org/abs/1908.11717
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 periodic background problem and the perturbed problem are modelled by
Externí odkaz:
http://arxiv.org/abs/1901.05102
In this article we develop a functional model for a general maximal dissipative operator. We construct the selfadjoint dilation of such operators. Unlike previous functional models, our model is given explicitly in terms of parameters of the original
Externí odkaz:
http://arxiv.org/abs/1804.08963
Autor:
Brown, B. M., Evans, W. D.
The self-adjoint and $m$-sectorial extensions of coercive Sturm-Liouville operators are characterised, under minimal smoothness conditions on the coefficients of the differential expression.
Comment: accepted by IEOT, in IEOT 2016
Comment: accepted by IEOT, in IEOT 2016
Externí odkaz:
http://arxiv.org/abs/1604.03170
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We discuss the detectable subspaces of an operator. We analyse the relation between the M-function (the abstract Dirichlet to Neumann map) and the resolvent bordered by projections onto the detectable subspaces. The abstract results are explored furt
Externí odkaz:
http://arxiv.org/abs/1404.6820
The spectrum of periodic differential operators typically exhibits a band-gap structure. In this paper, we will consider perturbations to periodic differential operators and investigate the spectrum the perturbation induces in the gaps. More specific
Externí odkaz:
http://arxiv.org/abs/1306.6256
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 the Neumann Lapla- cian in certain Rooms and Passages domains the seco
Externí odkaz:
http://arxiv.org/abs/1301.4396
In this paper, we combine results on extensions of operators with recent results on the relation between the M-function and the spectrum, to examine the spectral behaviour of boundary value problems. M-functions are defined for general closed extensi
Externí odkaz:
http://arxiv.org/abs/0803.3630
Autor:
Brown, B. M., Weikard, R.
We prove that a compactly supported perturbation of a rational or simply periodic algebro-geometric potential of the one-dimensional Schr\"odinger equation on the half line is uniquely determined by the location of its Dirichlet eigenvalues and reson
Externí odkaz:
http://arxiv.org/abs/math-ph/0306003