数学物理学报(英文版) ›› 1990, Vol. 10 ›› Issue (4): 402-411.
阳名珠, 姚爱翔
Yang Mingzhu, Yao Aixiang
摘要: The eigenvalue problem of the transport operator for a general bounded convex body V is studied mathematically. Where either V or the eigenfunction of the operator is not necessarily of spherical symmetry.It is shown that the spectrum of the operator consists of pure eigenvalues, possibly plusthe point of negative infinity.There is a countable infinity of real eigenvalues accumulating at minus infinity. Each eigenvalue, especially one in the left half-plane, is of index one, There is no complex (non-real) eigenvalue in the right half-plane Re λ>-Σ. The solution of the corresponding initial-value problem is also discussed.