References
Albertoni, S., Montagnini, B.: On the spectrum of neutron transport equation in finite bodies. J. Math. Anal. Appl.13, 19–48 (1966)
Aliprantis, C.D., Burkinshaw, O.: Positive compact operators on Banach lattices. Math. Z.174, 289–298 (1980)
Angelescu, N., Protopopescu, V.: On a problem in linear transport theory. Rev. Roumaine Phys.22, 1056–1061 (1977)
Birkhoff, G.: Positivity and criticality. Proc. Symp. Appl. Math.10, pp. 116–126. Providence: Amer. Math. Soc. 1959
Davies, E.B.: One — Parameter Semigroups. London-New York: Academic Press 1980
Derndinger, R.: Über das Spektrum positiver Generatoren. Math. Z.172, 281–293 (1980)
Dodds, P.G., Fremlin, D.H.: Compact operators in Banach lattices. Israel J. Math.34, 287–320 (1979)
Dunford, N., Schwartz, J.T.: Linear Operators, Part I. New York: Wiley 1958
Greiner, G.: Zur Perron-Frobenius-Theorie stark stetiger Halbgruppen. Math. Z.177, 401–423 (1981)
Greiner, G.: Spektrum und Asymptotik stark stetiger Halbgruppen positiver Operatoren. Sitzungsber. Heidelb. Akad. Wiss. Math.-Nat. Kl., 3. Abh. 1982
Greiner, G.: Asymptotics in linear transport theory. Semesterbericht Funktionalanalysis, Tübingen Sommersem. 1982
Greiner, G., Voigt, J., Wolff, M.: On the spectral bound of the generator of semigroups of positive operators. J. Operator Theory5, 245–256 (1981)
Jörgens, K.: An asymptotic expansion in the theory of neutron transport. Comm. Pure Appl. Math.11, 219–242 (1958)
Kaper, H.G., Lekkerkerker, C.G., Hejtmanek, J.: Spectral methods in linear transport theory. Basel: Birkhäuser 1982
Larsen, E.W.: The spectrum of the multigroup transport operator. J. Math. Phys.20, 1776–1782 (1979)
Larsen, E.W., Zweifel, P.F.: On the spectrum of the linear transport operator. J. Math. Phys.15, 1987–1997 (1974)
Lehner, L., Wing, G.M.: On the spectrum of an unsymmetric operator arising in the transport theory of neutrons. Comm. Pure Appl. Math.8, 217–234 (1955)
Marek, I.: Fundamental decay mode and asymptotic behavior of positive semigroups. Czechoslovak Math. J.30, 579–590 (1980)
Nagel, R., Schlotterbeck, U.: Kompaktheit von Integraloperatoren auf Banachverbänden. Math. Ann.202, 301–306 (1973)
Pao, C.V.: Asymptotic behavior of the solution for the time-dependent neutron transport problem. J. Integral Equations1, 131–152 (1979)
Schaefer, H.H.: Banach Lattices and Positive Operators. Berlin-Heidelberg-New York: Springer 1974
Vidav, I.: Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator. J. Math. Anal. Appl.22, 144–155 (1968)
Vidav, I.: Spectra of perturbed semigroups with applications to transport theory. J. Math. Anal. Appl.30, 264–279 (1970)
Voigt, J.: A perturbation theorem for the essential spectral radius of strongly continuous semigroups. Monatsh. Math.90, 153–161 (1980)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Greiner, G. Spectral properties and asymptotic behavior of the linear transport equation. Math Z 185, 167–177 (1984). https://doi.org/10.1007/BF01181687
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01181687