On the discrete spectrum of a linear operator pencil arizing in transport theory. (English) Zbl 1313.47039

Cojuhari, P. A.

Methods Funct. Anal. Topol. 20, No. 1, 10-16 (2014).

The author finds new sufficient conditions for the finiteness of the discrete spectrum for a linear operator pencil occurring in one-velocity transport theory. The technique is based on abstract perturbation theory. For earlier results in this direction, see K. M. Case [J. Math. Phys. 15, 974–983 (1974; Zbl 0293.45004)]; C. G. Lekkerkerker [Integral Equations Oper. Theory 4, 245–274 (1981; Zbl 0459.47005)].

Reviewer: Anatoly N. Kochubei (Kyïv)

MSC:

47A75	Eigenvalue problems for linear operators
47A55	Perturbation theory of linear operators
82C70	Transport processes in time-dependent statistical mechanics

Keywords:

operator pencil; transport equation

Citations:

Zbl 0293.45004; Zbl 0459.47005