Acta mathematica scientia,Series B ›› 1990, Vol. 10 ›› Issue (4): 402-411.
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Yang Mingzhu, Yao Aixiang
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Abstract: 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.
Yang Mingzhu, Yao Aixiang. ON THE SPECTRUM OF THE TRANSPORT OPERATOR FOR A BOUNDED CONVEX BODY[J].Acta mathematica scientia,Series B, 1990, 10(4): 402-411.
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