Far Eastern Mathematical Journal

To content of the issue


Study of spectral properties of a translation operator


V. I. Zhukova, L. N. Gamolja

2004, issue 1, P. 158–164


Abstract
The resolvent for a translation operator is constructed. The evaluation of its norm is obtained. From an evaluation follows, that the translation operator is a yielding operator strongly of continuous group of operators.

Keywords: translation operator, closure, resolvent, spectrum

Download the article (PDF-file)

References

[1] J. Lehner, G. Wing, “On the spectrum of an unsymmetric operator arising in the transport theory of neutrons”, Comm. Pure Appl. Math., 8 (1955), 217–234.
[2] J. Lehner, G. Wing, “Solution of the linearized Boltzmann equation for the slab geometry”, Duke Math. J., 23 (1956), 125–142.
[3] Dzh. M. Ving, “Kineticheskaya teoriya i spektral'nye problemy”, Teoriya yadernyx reaktorov, red. G. Birkxof, E'. Vigner, M., 1963, 160.
[4] K. Jorgens, “An Asimptotic expansion in the theory of neutron transport”, Comm. Pure Appl. Math., 11 (1958), 219.
[5] S. B. Shixov, “Nekotorye voprosy matematicheskoj teorii kriticheskogo sostoyaniya reaktora”, Zh. vychisl. matematiki i matem. fiz., 7:1 (1967), 113–127.
[6] S. B. Shixov, Voprosy matematicheskoj teorii reaktorov. Linejnyj analiz, Atomizdat, M., 1973, 375 s.
[7] J. Lehner, “The spectrum of neutron transport operator for the infinite slab”, J. Math. Mech., 11:2 (1962), 173–181.
[8] V. I. Zhukova, “Issledovaniya spektral'nyx svojstv operatora perenosa”, Sbornik trudov nauchno-prakticheskoj konferencii DVGUPS, t. 2, Xabarovsk, 1997, 180–181 s.
[9] Yu. A. Kuperin, S. N. Naboko, R. V. Romanov, “Spektral'nyj analiz odnoskorostnogo operatora perenosa i funkcional'naya model'”, Funkcional'nyj analiz i ego prilozheniya, 33:3 (1999), 47–58.
[10] V. I. Zhukova, “Spektral'nye svojstva operatora perenosa”, Trudy vserossijskoj nauchno-prakticheskoj konferencii, t. 5, Chita, 2000, 170–174.
[11] E'. Xille, R. Fillips, Funkcional'nyj analiz i polugruppy, IL, M., 1962, 829 s.
[12] K. Iosida, Funkcional'nyj analiz, Mir, M., 1967, 624 s.

To content of the issue