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Estimates of solutions of linear neutron transport equation at large time and spectral singularities
1. | Laboratory of Quantum Networks and Department of Mathematical Physic, Faculty of Physics, St.Petersburg State University, 198504, Saint Petersburg, Russian Federation |
References:
[1] |
B. Sz.-Nagy and C. Foiaş, "Analyse Harmonique des Opérateurs de l'Espase de Hilbert," (French) [Harmonic Analysis of Operators in Hilbert Space], Masson et Cie, Paris, Académiai Kiadó, Budapest, 1967. |
[2] |
J. Lehner, The spectrum of the neutron transport operator for the infinite slab, J. Math. Mech., 11 (1962), 173-181. |
[3] |
J. Lehner and G. Wing, On the spectrum of an unsymmetric operator arising in the transport theory of neutrons, Comm. Pure Appl. Math., 8 (1955), 217-234.
doi: 10.1002/cpa.3160080202. |
[4] |
J. Lehner and G. Wing, Solution of the linearized Boltzmann transport equation for the slab geometry, Duke Math. J., 23 (1956), 125-142.
doi: 10.1215/S0012-7094-56-02312-2. |
[5] |
Yu. Kuperin, S. Naboko and R. Romanov, Spectral analysis of the transport operator: A functional model approach, Indiana Univ. Math. J., 51 (2002), 1389-1425.
doi: 10.1512/iumj.2002.51.2180. |
[6] |
B. S. Pavlov, On separation conditions for the spectral components of a dissipative operator, Izv. Akad. Nauk SSSR Ser. Mat., 39 (1975), 123-148, 240. |
[7] |
M. A. Naĭmark, Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoint differential operator of the second order on a semi-axis, (Russian) Trudy Mosk. Mat. Obšč., 3 (1954), 181-270; English transl., Amer. Math. Soc. Transl. (2), 16 (1960), 103-193. |
[8] |
B. S. Pavlov, Spectral analysis of a dissipative singular Schrödinger operator in terms of a functional model, in "Partial Differential Equations, VIII" (ed. M. Shubin), Encyclopaedia Math. Sci., 65, Springer, Berlin, (1996), 87-153. |
[9] |
S. N. Naboko, Functional model of perturbation theory and its applications to scattering theory, (Russian) Boundary value problems of mathematical physics, 10, Trudy Mat. Inst. Steklov, 147 (1980), 86-114, 203; English transl., Proc. Steklov Inst. Math., 147 (1981), 85-116. |
[10] |
S. N. Naboko, On the conditions for existence of wave operators in the nonselfadjoint case, (Russian) in "Wave Propagation. Scattering Theory" (ed. M. Birman), LGU, Leningrad, (1987), 132-155; English transl., Amer. Math. Soc. Transl. Ser. 2, 157, AMS, Providence, RI, (1993), 127-149. |
[11] |
S. Naboko and R. Romanov, Spectral singularities and asymptotics of contractive semigroups. I, Acta Sci. Math. (Szeged), 70 (2004), 379-403. |
[12] |
N. K. Nikol'skiĭ , "Treatise on the Shift Operator. Spectral Function Theory," With an appendix by S. V. Hruščev [S. V. Khrushchëv] and V. V. Peller, Translated from the Russian by Jaak Peetre, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 273, Springer-Verlag, Berlin, 1986. |
[13] |
R. Romanov, A remark on equivalence of weak and strong definitions of the absolutely continuous subspace for nonself-adjoint operators, in "Spectral Methods for Operators of Mathematical Physics" (Bedlewo, 2002), Oper. Theory Adv. Appl., 154, Birkhäuser, Basel, (2004), 179-184. |
[14] |
L. A.Sahnovič, Dissipative operators with absolutely continuous spectrum, (Russian) Trudy Moskov. Mat. Obšč., 19 (1968), 211-270. |
[15] |
A. S. Tikhonov, Functional model and duality of spectral components for operators with continuous spectrum on a curve, (Russian) Algebra i Analiz, 14 (2002), 158-195; English transl., St. Petersburg Math. J., 14 (2003), 655-682. |
[16] |
R. Romanov and M. Tihomirov, On the selfadjoint subspace of the one-velocity transport operator, Math. Notes, 89 (2011), 106-116.
doi: 10.1134/S0001434611010111. |
show all references
References:
[1] |
B. Sz.-Nagy and C. Foiaş, "Analyse Harmonique des Opérateurs de l'Espase de Hilbert," (French) [Harmonic Analysis of Operators in Hilbert Space], Masson et Cie, Paris, Académiai Kiadó, Budapest, 1967. |
[2] |
J. Lehner, The spectrum of the neutron transport operator for the infinite slab, J. Math. Mech., 11 (1962), 173-181. |
[3] |
J. Lehner and G. Wing, On the spectrum of an unsymmetric operator arising in the transport theory of neutrons, Comm. Pure Appl. Math., 8 (1955), 217-234.
doi: 10.1002/cpa.3160080202. |
[4] |
J. Lehner and G. Wing, Solution of the linearized Boltzmann transport equation for the slab geometry, Duke Math. J., 23 (1956), 125-142.
doi: 10.1215/S0012-7094-56-02312-2. |
[5] |
Yu. Kuperin, S. Naboko and R. Romanov, Spectral analysis of the transport operator: A functional model approach, Indiana Univ. Math. J., 51 (2002), 1389-1425.
doi: 10.1512/iumj.2002.51.2180. |
[6] |
B. S. Pavlov, On separation conditions for the spectral components of a dissipative operator, Izv. Akad. Nauk SSSR Ser. Mat., 39 (1975), 123-148, 240. |
[7] |
M. A. Naĭmark, Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoint differential operator of the second order on a semi-axis, (Russian) Trudy Mosk. Mat. Obšč., 3 (1954), 181-270; English transl., Amer. Math. Soc. Transl. (2), 16 (1960), 103-193. |
[8] |
B. S. Pavlov, Spectral analysis of a dissipative singular Schrödinger operator in terms of a functional model, in "Partial Differential Equations, VIII" (ed. M. Shubin), Encyclopaedia Math. Sci., 65, Springer, Berlin, (1996), 87-153. |
[9] |
S. N. Naboko, Functional model of perturbation theory and its applications to scattering theory, (Russian) Boundary value problems of mathematical physics, 10, Trudy Mat. Inst. Steklov, 147 (1980), 86-114, 203; English transl., Proc. Steklov Inst. Math., 147 (1981), 85-116. |
[10] |
S. N. Naboko, On the conditions for existence of wave operators in the nonselfadjoint case, (Russian) in "Wave Propagation. Scattering Theory" (ed. M. Birman), LGU, Leningrad, (1987), 132-155; English transl., Amer. Math. Soc. Transl. Ser. 2, 157, AMS, Providence, RI, (1993), 127-149. |
[11] |
S. Naboko and R. Romanov, Spectral singularities and asymptotics of contractive semigroups. I, Acta Sci. Math. (Szeged), 70 (2004), 379-403. |
[12] |
N. K. Nikol'skiĭ , "Treatise on the Shift Operator. Spectral Function Theory," With an appendix by S. V. Hruščev [S. V. Khrushchëv] and V. V. Peller, Translated from the Russian by Jaak Peetre, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 273, Springer-Verlag, Berlin, 1986. |
[13] |
R. Romanov, A remark on equivalence of weak and strong definitions of the absolutely continuous subspace for nonself-adjoint operators, in "Spectral Methods for Operators of Mathematical Physics" (Bedlewo, 2002), Oper. Theory Adv. Appl., 154, Birkhäuser, Basel, (2004), 179-184. |
[14] |
L. A.Sahnovič, Dissipative operators with absolutely continuous spectrum, (Russian) Trudy Moskov. Mat. Obšč., 19 (1968), 211-270. |
[15] |
A. S. Tikhonov, Functional model and duality of spectral components for operators with continuous spectrum on a curve, (Russian) Algebra i Analiz, 14 (2002), 158-195; English transl., St. Petersburg Math. J., 14 (2003), 655-682. |
[16] |
R. Romanov and M. Tihomirov, On the selfadjoint subspace of the one-velocity transport operator, Math. Notes, 89 (2011), 106-116.
doi: 10.1134/S0001434611010111. |
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