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 lambda > -SIGMA. The solution of the corresponding initial-value problem is also discussed.
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 lambda > -SIGMA. The solution of the corresponding initial-value problem is also discussed.
基金
This project was supported by National Natural Science Foundation of China.
