Geodesic
On the Self-Adjoint Subspace of the One-Velocity Transport Operator
Matematičeskie zametki, Tome 89 (2011) no. 1, pp. 91-103.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the problem of describing the self-adjoint subspace of the transport operator in an unbounded domain. It is proved that this subspace is nontrivial under perturbations having a gap lattice of arbitrarily small length for the one-velocity operator with polynomial collision integral. We also consider the three-dimensional transport operator.
Keywords: transport operator, collision integral, self-adjoint subspace
Mots-clés : Lebesgue spectrum, isomorphism. 
@article{MZM_2011_89_1_a8,
     author = {R. V. Romanov and M. A. Tikhomirov},
     title = {On the {Self-Adjoint} {Subspace} of the {One-Velocity} {Transport} {Operator}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {91--103},
     publisher = {mathdoc},
     volume = {89},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_1_a8/}
}
TY  - JOUR
AU  - R. V. Romanov
AU  - M. A. Tikhomirov
TI  - On the Self-Adjoint Subspace of the One-Velocity Transport Operator
JO  - Matematičeskie zametki
PY  - 2011
SP  - 91
EP  - 103
VL  - 89
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2011_89_1_a8/
LA  - ru
ID  - MZM_2011_89_1_a8
ER  - 
%0 Journal Article
%A R. V. Romanov
%A M. A. Tikhomirov
%T On the Self-Adjoint Subspace of the One-Velocity Transport Operator
%J Matematičeskie zametki
%D 2011
%P 91-103
%V 89
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2011_89_1_a8/
%G ru
%F MZM_2011_89_1_a8
R. V. Romanov; M. A. Tikhomirov. On the Self-Adjoint Subspace of the One-Velocity Transport Operator. Matematičeskie zametki, Tome 89 (2011) no. 1, pp. 91-103. http://geodesic.mathdoc.fr/item/MZM_2011_89_1_a8/

[1] J. Lehner, “The spectrum of the neutron transport operator for the infinite slab”, J. Math. Mech., 11:2 (1962), 173–181 | MR | Zbl

[2] S. B. Shikhov, Voprosy matematicheskoi teorii reaktorov. Lineinyi analiz, Atomizdat, M., 1973

[3] B. Sekefalvi-Nad, Ch. Foyash, Garmonicheskii analiz operatorov v gilbertovom prostranstve, Mir, M., 1970 | MR | Zbl

[4] S. N. Naboko, “Funktsionalnaya model teorii vozmuschenii i ee prilozheniya k teorii rasseyaniya”, Kraevye zadachi matematicheskoi fiziki. 10, Sbornik rabot, Tr. MIAN SSSR, 147, 1980, 86–114 | MR | Zbl

[5] J. Lehner, G. M. Wing, “On the spectrum of an unsymmetric operator arising in the transport theory of neutrons”, Comm. Pure Appl. Math., 8:2 (1955), 217–234 | DOI | MR | Zbl

[6] Yu. A. Kuperin, S. N. Naboko, R. V. Romanov, “Spectral analysis of the transport operator: a functional model approach”, Indiana Univ. Math. J., 51:6 (2002), 1389–1425 | DOI | MR | Zbl

[7] V. Havin, B. Jöricke, The Uncertainty Principle in Harmonic Analysis, Ergeb. Math. Grenzgeb. (3), 28, Springer-Verlag, Berlin, 1994 | MR | Zbl

[8] P. P. Kargaev, “Preobrazovanie Fure kharakteristicheskoi funktsii mnozhestva, ischezayuschee na intervale”, Matem. sb., 117:3 (1982), 397–411 | MR | Zbl

[9] M. Mitkovski, A. Poltoratski, Polya Sequences, Toeplitz Kernels and Gap Theorems, arXiv: math.CV/0903.4499

[10] V. V. Kozlov, Teplovoe ravnovesie po Gibbsu i Puankare, Sovremennaya matematika, IKI, M.–Izhevsk, 2002 | MR | Zbl