Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MZM_2016_100_1_a4, author = {A. S. Kostenko and M. M. Malamud and D. D. Natyagajlo}, title = {Matrix {Schr\"odinger} {Operator} with $\delta${-Interactions}}, journal = {Matemati\v{c}eskie zametki}, pages = {59--77}, publisher = {mathdoc}, volume = {100}, number = {1}, year = {2016}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a4/} }
TY - JOUR AU - A. S. Kostenko AU - M. M. Malamud AU - D. D. Natyagajlo TI - Matrix Schr\"odinger Operator with $\delta$-Interactions JO - Matematičeskie zametki PY - 2016 SP - 59 EP - 77 VL - 100 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a4/ LA - ru ID - MZM_2016_100_1_a4 ER -
A. S. Kostenko; M. M. Malamud; D. D. Natyagajlo. Matrix Schr\"odinger Operator with $\delta$-Interactions. Matematičeskie zametki, Tome 100 (2016) no. 1, pp. 59-77. http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a4/
[1] F. S. Rofe-Beketov, A. M. Kholkin, Spectral Analysis of Differential Operators. Interplay Between Spectral and Oscillatory Properties, World Sci. Monogr. Ser. in Math., 7, World Sci., Singapore, 2005 | MR | Zbl
[2] V. I. Gorbachuk, M. L. Gorbachuk, Granichnye zadachi dlya differentsialno-operatornykh uravnenii, Naukova dumka, Kiev, 1984 | MR | Zbl
[3] A. M. Savchuk, A. A. Shkalikov, “Operatory Shturma–Liuvillya s potentsialami-raspredeleniyami”, Tr. MMO, 64, MTsNMO, M., 2003, 159–212 | MR | Zbl
[4] K. A. Mirzoev, T. A. Safonova, “Singulyarnye operatory Shturma–Liuvillya s potentsialami-raspredeleniyami v prostranstve vektor-funktsii”, Dokl. RAN, 441:2 (2011), 165–168 | MR | Zbl
[5] K. A. Mirzoev, T. A. Safonova, “Singulyarnye operatory Shturma–Liuvillya s negladkimi potentsialami v prostranstve vektor-funktsii”, Ufimsk. matem. zhurn., 3:3 (2011), 105–119 | MR | Zbl
[6] K. A. Mirzoev, “Operatory Shturma–Liuvillya”, Tr. MMO, 75, no. 2, MTsNMO, M., 2014, 335–359 | Zbl
[7] J. Eckhardt, F. Gesztesy, R. Nichols, G. Teschl, “Weyl–Titchmarsh theory for Sturm–Liouville operators with distributional potentials”, Opuscula Math., 33:3 (2013), 467–563 | DOI | MR | Zbl
[8] J. Eckhardt, F. Gesztesy, R. Nichols, G. Teschl, “Supersymmetry and Schrödinger-type operators with distributional matrix-valued potentials”, J. Spectr. Theory, 4:4 (2014), 715–768 | DOI | MR | Zbl
[9] S. Albeverio, F. Gesztesy, R. Høegh-Krohn, H. Holden, Solvable Models in Quantum Mechanics, With an appendix by Pavel Exner, 2nd edition, Amer. Math. Soc., Providence, RI, 2004 | MR
[10] A. C. Kostenko, M. M. Malamud, “Ob odnomernom operatore Shredingera s $\delta$-vzaimodeistviyami”, Funkts. analiz i ego pril., 44:2 (2010), 87–91 | DOI | MR | Zbl
[11] A. S. Kostenko, M. M. Malamud, “1–D Schrödinger operators with local point interactions on discrete set”, J. Differential Equations, 249:2 (2010), 253–304 | DOI | MR | Zbl
[12] S. Albeverio, A. Kostenko, M. Malamud, “Spectral theory of semi-bounded Sturm–Liouville operators with local interactions on a discrete set”, J. Math. Phys., 51:10 (2010), 102102 | MR
[13] A. Kostenko, M. Malamud, “1–D Schrödinger operators with local point interactions: a review”, Spectral Analysis, Differential Equations and Mathematical Physics: a Festschrift in Honor of Fritz Gesztesy's 60th Birthday, Proc. Symp. Pure Math., 87, Amer. Math. Soc., Providence, RI, 2013, 235–262 | DOI | MR | Zbl
[14] V. A. Derkach, M. M. Malamud, “Generalized resolvents and the boundary value problems for hermitian operators with gaps”, J. Funct. Anal., 95:1 (1991), 1–95 | DOI | MR | Zbl
[15] M. M. Malamud, “O nekotorykh klassakh rasshirenii ermitovykh operatorov s lakunami”, Ukr. matem. zhurn., 44:2 (1992), 215–233 | MR | Zbl
[16] N. I. Akhiezer, Klassicheskaya problema momentov i nekotorye voprosy analiza, svyazannye s neyu, Fizmatgiz, M., 1961 | MR | Zbl
[17] Yu. M. Berezanskii, Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, Naukova dumka, Kiev, 1965 | MR | Zbl
[18] A. G. Kostyuchenko, K. A. Mirzoev, “Trekhchlennye rekurrentnye sootnosheniya s matrichnymi koeffitsientami. Vpolne neopredelennyi sluchai”, Matem. zametki, 63:5 (1998), 709–716 | DOI | MR | Zbl
[19] A. G. Kostyuchenko, K. A. Mirzoev, “Obobschennye yakobievy matritsy i indeksy defekta obyknovennykh differentsialnykh operatorov s polinomialnymi koeffitsientami”, Funkts. analiz i ego pril., 33:1 (1999), 30–45 | DOI | MR | Zbl
[20] A. G. Kostyuchenko, K. A. Mirzoev, “Priznaki vpolne neopredelennosti yakobievykh matrits s matrichnymi elementami”, Funkts. analiz i ego pril., 35:4 (2001), 32–37 | DOI | MR | Zbl
[21] M. Malamud, H. Neidhardt, “Sturm-Liouville boundary value problems with operator potentials and unitary equivalence”, J. Differential Equations, 252:11 (2011), 5875–5922 | DOI | MR
[22] R. Carlone, M. Malamud, A. Posilicano, “On the spectral theory of Gesztezy–Šeba realizations of 1-D Dirac operators with point interactions on discrete set”, J. Differential Equations, 254 (2013), 3835–3902 | DOI | MR | Zbl
[23] Yu. M. Dyukarev, “O defektnykh chislakh simmetricheskikh operatorov, porozhdennykh blochnymi matritsami Yakobi”, Matem. sb., 197:8 (2006), 73–100 | DOI | MR | Zbl
[24] Yu. M. Dyukarev, “Primery blochnykh matrits Yakobi, porozhdayuschikh simmetricheskie operatory s lyubymi vozmozhnymi defektnymi chislami”, Matem. sb., 201:12 (2010), 83–92 | DOI | MR | Zbl
[25] V. I. Kogan, “Ob operatorakh, porozhdennykh $I_p$-matritsami v sluchae maksimalnykh indesov defekta”, Teoriya funktsii, funkts. analiz i ikh pril., 11 (1970), 103–107 | MR | Zbl
[26] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki. T. 3. Teoriya rasseyaniya, Mir, M., 1982 | MR