On the discrete spectrum of a linear operator pencil arising in transport theory

Abstract

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.

Full Text

Article Information

Title	On the discrete spectrum of a linear operator pencil arising in transport theory
Source	Methods Funct. Anal. Topology, Vol. 20 (2014), no. 1, 10-16
MathSciNet	MR3242119
zbMATH	1313.47039
Milestones	Received 30/09/2013
Copyright	The Author(s) 2014 (CC BY-SA)

Authors Information

P. A. Cojuhari
Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland

Citation Example

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},
}