We study the problem of the finiteness of the discrete spectrum for linear operator pencils occurring in one-velocity transport theory. The results are obtained using direct methods of perturbation theory for linear operators. The proposed approach allowed to give a relatively quick proofs of the main results improving related results obtained previously by K. M. Case and C. G. Lekkerkerker.
Key words: Spectral theory, compact perturbation, operator pencil, transport equation.
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Article Information
Title
On the discrete spectrum of a linear operator pencil arising in transport theory
P. A. Cojuhari, On the discrete spectrum of a linear operator pencil arising in transport theory, Methods Funct. Anal. Topology 20
(2014), no. 1, 10-16.
BibTex
@article {MFAT711,
AUTHOR = {Cojuhari, P. A.},
TITLE = {On the discrete spectrum of a linear operator pencil arising in transport theory},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {20},
YEAR = {2014},
NUMBER = {1},
PAGES = {10-16},
ISSN = {1029-3531},
MRNUMBER = {MR3242119},
ZBLNUMBER = {1313.47039},
URL = {http://mfat.imath.kiev.ua/article/?id=711},
}