Spectral properties and finite range elementary solutions of the linear Boltzmann equation
C. Syros · Bulletin de la Classe des sciences · 1973
The property of the operator (zδx + 1) to transform a definite class of functions ψ(x,z ) depending on two variables to functions ψ(x) depending only on one variable allows the algebraic determination of the spectral properties of the Boltzmann equation in a finite domain of R1. A number of theorems have been proved regarding the spectrum of characteristic values. In the case of homogeneous boundary conditions the spectral property [formule] has been established, where [formule] satisfy [formule]. The eigenfunctions are under certain conditions invariant against parity, scaling and translation transformation.