On instability of the absolutely continuous spectrum of dissipative Schr\"odinger operators and Jacobi matrices
Algebra i analiz, Tome 17 (2005) no. 2, pp. 145-169.

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

@article{AA_2005_17_2_a6,
     author = {R. V. Romanov},
     title = {On instability of the absolutely continuous spectrum of dissipative {Schr\"odinger} operators and {Jacobi} matrices},
     journal = {Algebra i analiz},
     pages = {145--169},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2005_17_2_a6/}
}
TY  - JOUR
AU  - R. V. Romanov
TI  - On instability of the absolutely continuous spectrum of dissipative Schr\"odinger operators and Jacobi matrices
JO  - Algebra i analiz
PY  - 2005
SP  - 145
EP  - 169
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2005_17_2_a6/
LA  - ru
ID  - AA_2005_17_2_a6
ER  - 
%0 Journal Article
%A R. V. Romanov
%T On instability of the absolutely continuous spectrum of dissipative Schr\"odinger operators and Jacobi matrices
%J Algebra i analiz
%D 2005
%P 145-169
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2005_17_2_a6/
%G ru
%F AA_2005_17_2_a6
R. V. Romanov. On instability of the absolutely continuous spectrum of dissipative Schr\"odinger operators and Jacobi matrices. Algebra i analiz, Tome 17 (2005) no. 2, pp. 145-169. http://geodesic.mathdoc.fr/item/AA_2005_17_2_a6/

[1] Deift P., Killip R., “On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials”, Comm. Math. Phys., 203 (1999), 341–347 | DOI | MR | Zbl

[2] Christ M., Kiselev A., “Scattering and wave operators for one-dimensional Schrödinger operators with slowly decaying nonsmooth potentials”, Geom. Funct. Anal., 12 (2002), 1174–1234 | DOI | MR | Zbl

[3] Naboko S. H., “Funktsionalnaya model teorii vozmuschenii i ee prilozheniya k teorii rasseyaniya”, Tr. Mat. in-ta AN SSSR, 147, 1980, 86–114 | MR | Zbl

[4] Naboko S. N., “Ob usloviyakh suschestvovaniya volnovykh operatorov v nesamosopryazhennom sluchae”, Probl. mat. fiz., 1987, no. 12, 132–155, LGU, L. | MR

[5] Sz.-Nagy B., Foiaš C., Analyse harmonique des opérateurs de l'espace de Hilbert, Masson et Cie, Akad. Kiadó, Paris, Budapest, 1967 | MR

[6] Pavlov B. S., “O razlozhenii po sobstvennym funktsiyam absolyutno nepreryvnogo spektra dissipativnogo operatora”, Vestn. Leningr. un-ta. Ser. mat., mekh., astronom., 1975, no. 1, 130–137 | MR | Zbl

[7] Sakhnovich L. A., “Dissipativnye operatory s absolyutno nepreryvnym spektrom”, Tr. Mosk. mat. o-va, 19, 1968, 211–270 | Zbl

[8] Pavlov B. S., “Samosopryazhennaya dilatatsiya dissipativnogo operatora Shredingera i razlozhenie po ego sobstvennym funktsiyam”, Mat. sb., 102(144):4 (1977), 511–536 | MR | Zbl

[9] Tikhonov A. S., Absolyutno nepreryvnyi spektr lineinogo operatora i zadachi teorii rasseyaniya i faktorizatsii operator-funktsii, Avtoref. dis. na soisk. uchen. st. kand. fiz.-mat. nauk, Simferopolskii gos. un-t, Simferopol, 1989 | MR

[10] Romanov R., “A remark on equivalence of weak and strong definitions of the absolutely continuous subspace for nonself-adjoint operators”, Oper. Theory Adv. Appl., 154, Birkhäuser, Basel, 2004, 179–184 | MR | Zbl

[11] Sims A. R., “Secondary conditions for linear differential operators of the second order”, J. Math. Mech., 6:2 (1957), 247–285 | MR | Zbl

[12] Eastham M. S. P., The asymptotic solution of linear differential systems, London Math. Soc. Monogr. New Ser., 4, The Clarendon Press, Oxford Univ. Press, New York, 1989 | MR

[13] Pearson D. B., Quantum scattering and spectral theory, Techn. Phys., 9, Acad. Press, London, 1988 | MR

[14] Last Y., Simon B., “Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators”, Invent. Math., 135:2 (1999), 329–367 | DOI | MR | Zbl

[15] Simon B., “Bounded eigenfunctions and absolutely continuous spectra for onedimensional Schrödinger operators”, Proc. Amer. Math. Soc., 124 (1996), 3361–3369 | DOI | MR

[16] Nikolskii H. K., Lektsii ob operatore sdviga, Nauka, M., 1980 | MR