Spectral properties of a streaming operator with diffuse reflection boundary condition
The author studies the spectrum of a streaming operator with diffuse reflection boundary condition arising in transport theory. This unbounded operator in \(L_1\) is associated with bounded integral operators determined by the boundary condition. The spectrum of the streaming operator is determined by these integral operators. It consist of a countable set of isolated eigenvalues with a finite algebraic multiplicity. Further, the diffuse reflection boundary condition of Maxwell type is considered. In this case the streaming operator has only one real eigenvalue which is simple and all complex eigenvalues have geometrical multiplicity one. A formula for computing these eigenvalues is given and the algebraic multiplicity of complex eigenvalues is discussed.
algebraic multiplicity of complex eigenvalues
scientific article; zbMATH DE number 1354748