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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Journal ArticleDOI
Compactness and norm continuity of the difference of two cosine functions
Miao Li,Bao-Zhu Guo,S. Piskarev +2 more
TL;DR: This paper showed that the compactness of the difference of two cosine functions can be characterized by the difference in resolvents of their resolvements, and made some comparisons between these results for C 0-semigroups and cosine function functions.
Posted Content
Global Well-posedness of the Relativistic Boltzmann Equation with Large Amplitude Initial Data
TL;DR: In this article, the authors proved the global existence and uniqueness of mild solutions to the relativistic Boltzmann equation in both whole space and torus for a class of initial data with bounded velocity-weighted $L^\infty$-norm under some additional smallness conditions on the defect mass, energy and entropy.
Book ChapterDOI
Fredholm Theory Related to Some Measures
TL;DR: In this paper, the concept of measures of noncompactness and measures of weak compactness has been studied in topology, functional analysis, and operator theory, and one axiomatic approach to this notion has been proposed.
Book ChapterDOI
Essential Spectra of 3 × 3 Block Operator Matrices
TL;DR: In this article, the essential spectra of operators defined by a 3 × 3 block operator matrix are studied, and the essential spectral properties of these operators are investigated. But they are not discussed in this paper.
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.