Spectra of perturbed semigroups with applications to transport theory
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This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1970-05-01 and is currently open access. It has received 156 citations till now. The article focuses on the topics: Linear transport theory & Neutron transport.read more
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Dissertation
Analyse spectrale de modèles neutroniques
TL;DR: In this article, the authors propose an approche, dite resolvante, de the stabilite des spectres essentiel and critique des semigroupes perturbes dans les espaces de Hilbert.
Book ChapterDOI
Spectral Graph Theory
TL;DR: The line graph of a given graph is so natural that it has been independently discovered by many authors as mentioned in this paper, and each author gave it a different name: interchange graph by Ore [272], derivative by H. Sachs [297], derived graph by L. W. Beineke [52], edge-to-vertex dual by M. Reed [291], coverning graph by G. Kirchhoff [189], and adjoint by V. Menon [247].
Book ChapterDOI
Eigenvalue Problems for the Boltzmann Operator in Various Formulations
TL;DR: In this paper, the authors present a review paper on the nature of various transport equation formulations and the role of eigenvalues, which is a collection of unsolved problems in transport theory published some years ago by Kaper and completed by another collection, due to Zweifel.
The nonaccretive radiative transfer equations: existence of solutionsand Rosseland approximation.
TL;DR: In this article, an existence theory and an asymptotic analysis for radiative transfer equations were presented, and it was shown that even if σ has a singularity (σ(0) = +∞), it has a solution ue ϵ L∞(R+ × X × SN).
Book ChapterDOI
Perturbation of linear semigroups
TL;DR: In this paper, an extension of a result on the essential spectral radius of a perturbed semigroup obtained by L. Weis is presented, and integral inequalities for the measure of non-compactness for strongly measurable operator-valued functions and linear semigroups are given.
References
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Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Journal ArticleDOI
On the spectrum of an unsymmetric operator arising in the transport theory of neutrons
Joseph Lehner,G. Milton Wing +1 more
Journal ArticleDOI
Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator
TL;DR: In this article, the authors considered the initial value problem and showed that the decay constant X is an eigenvalue of the Boltzmann operator A. The exact domain of definition of A is dependent on the space of functions where A acts, and will be described in Section 2.