On the spectral decompositions of the linear transport operator with periodic boundary conditions
Tóm tắt
It is shown that the linear transport operator for a slab with periodic boundary conditions, or for infinite medium, can be analyzed within the Friedrichs' model of perturbation for non-selfadjoint operators. This leads to rephrasing Case's generalized eigenfunction expansion in terms of Hilbert space operators only.
Tài liệu tham khảo
Angelescu, N., Marninescu, N., and Protopopescu, V., Transp. Th. Stat. Phys. 5, N03 (1976). (to appear).
Beleni-MoranteA., J. Math. Anal. Appl. 30, 353 (1970).
CaseK.M., Ann. Phys. (N.Y.) 9, 1 (1960).
CaseK.M. and ZweifelP.M., Linear Transport Theory, Addison-Wesley Publishing Co., Reading, Massachusetts, 1967, Chapter 7.
ZweifelP.M., Transp. Th. Stat. Phys. 3, 65 (1973).
DunfordN. and SchwartzJ.T., Linear Operators, Wiley-Interscience, New-York, Part II, 1963, Part III, 1971.
FriedrichsK.O., Commun. Pure Appl. Math. 1, 361 (1948).
SchwartzJ., Commun. Pure Appl. Math. 13, 609 (1960).
MochizukiK., J. Math. Soc. Japan 19, 123 (1967).
BeauwensR. and MikaJ., Nukleonika 14, 461 (1969).