Fundamental decay mode and asymptotic behaviour of positive semigroups
Czechoslovak Mathematical Journal, Tome 30 (1980) no. 4, pp. 579-590

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DOI : 10.21136/CMJ.1980.101706
Classification : 34G10, 47D05, 82A70
Marek, Ivo. Fundamental decay mode and asymptotic behaviour of positive semigroups. Czechoslovak Mathematical Journal, Tome 30 (1980) no. 4, pp. 579-590. doi: 10.21136/CMJ.1980.101706
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[1] Albertoni S., Montagnini В.: On the spectrum of neutron transport equation in finite bodies. J. Math. Anal. Appl. 13, 19-48, 1966. | DOI | MR | Zbl

[2] Hille E., Phillips R. S.: Functional Analysis and Semigroups. Revised Edition, American Math. Soc. Colloq. Publ. Vol. XXXI, Providence, 1957. | MR | Zbl

[3] Jörgens K.: On asymptotic expansion in the theory of neutron transport. Comm. Pure Appl. Math. 11, 219-242, 1957. | DOI | MR

[4] Kaper H. G.: A collection of problems in transport theory. Transport Theory and Stat. Physics 4, 13, 125-134, 1975. | DOI | MR

[5] Krein M. G., Rutman M. A.: Linear operators leaving invariant a cone in a Banach space. Uspekhi mat. nauk. III, N1, 3 - 95, 1948, (Russian). English translation in Amer. Math. Soc. Translations No. 26, pp. 128, 1950. | MR | Zbl

[6] Larsen E. W., Zweifel P. F.: On the spectrum of the linear transport operator. J. Math.-Phys. 15, 1987-1997, 1974. | DOI | MR

[7] Lehner J.: An unsymmetric operator arising in the theory of neutron diffusion. Comm. Pure Appl. Math. 9, 487-497, 1956. | DOI | MR | Zbl

[8] Lehner J., 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. | MR | Zbl

[9] Lehner J., Wing G. M.: Solution of the linearized Boltzman equation for the slab geometry. Duke Math. J. 23, 125-142, 1956. | MR

[10] Marek I.: Frobenius theory of positive operators. Comparison theorems and applications. SIAM J. Appl. Math. 19, 607-628, 1970. | DOI | MR | Zbl

[11] Marek I.: On some spectral properties of Radon-Nikolskii operators and their generalizations. Comment. Math. Univ. Carol. 3: 1, 20-30, 1962. | MR

[12] Niiro F., Sawashima I.: On spectral properties of positive irreducible operators in an arbitrary Banach lattice and problems of H. H. Schaefer. Sci. Papers College Gen. Educ., Univ. of Tokyo, 16, 145-183, 1966. | MR

[13] Sawashima I.: Spectral properties of some positive operators. Natur. Sci. Rep. Ochanomizu Univ. 15. 55-64, 1964. | MR | Zbl

[14] Schaefer H. H.: Banach Lattices and Positive Operators. Springer Verlag, Berlin-Heidelberg-New York, 1974. | MR | Zbl

[15] Shikhov S. В.: Lectures in Mathematical Theory of Reactors. I. Linear Theory. Atomizdat, Moscow, 1973 (Russian).

[16] Shizuta Y.: On the classical solutions of the Boltzmann equation. Preprint 1977. | MR

[17] Taylor A. E.: Introduction to Functional Analysis. J. Wiley Publ., New York, 1958. | MR | Zbl

[18] Ukai S.: On the existence of global solutions of mixed problem from non-linear Boltzmann equation. Proc. Japan Acad. 50, 179-184, 1974. | MR

[19] Vidav I.: Existence and uniqueness of non-negative eigenfunctions of the Boltzmann operator. J. Math. Anal. Appl. 22, 144-155, 1968. | DOI | MR

[20] Vidav I.: Spectra of perturbed semigroups with applications to transport theory. J. Math. Anal. Appl. 30, 264-279, 1970. | DOI | MR | Zbl

[21] Wing G. M.: An Introduction to Transport Theory. J. Wiley Publ., New York, 1962. | MR

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