Rank One Strong Singular Perturbation by Nonsymmetric Potential

For a rank one strong singular perturbation of a self-adjoint operator by nonsymmetric potential, we present a construction and investigated the corresponding eigenvalue problem.

Publication year: 
2014
Issue: 
4
УДК: 
517.9
С. 13–16., Бібліогр.: 8 назв.
References: 

1. S. Albeverio and P. Kurasov, “Singular perturbations of differential operators. Solvable Schrцdinger type operators”, in London Math. Soc. Lecture Note Series, Cambridge: Cambridge University Press, 2000, vol. 271, xiv+429 pp.
2. S. Albeverio et al., Solvable models in quantum mechanics, 2nd ed., AMS Chelsea Publishing, Providence, RI, 2005, xiv+488 pp.
3. Кошманенко В.Д., Дудкін М.Е. Метод оснащених просторів у теорії сингулярних збурень самоспряжених операторів. — К.: Ін-т математики НАНУ, 2013. — 320 c.
4. T. Kato and J.B. McLeod, “The functional-differential equation y′(x) ay (λx) by (x) ”, Bull. Amer. Math. Soc., vol. 77, pp. 891—937, 1971.
5. V. Koshmanenko, Singular quadratic forms in perturbation theory (translated from the 1993 russian original by P.V. Malyshev and D.V. Malyshev), Mathematics and its Applications, vol. 474, pp. viii+308, 1999.
6. L.P. Nizhnik, “On rank one singular perturbations of selfadjoint operators”, Ibid, vol. 7, no. 3, pp. 54—66, 2001.
7. M.M. Malamud and V.I. Mogilevskii, “Kreĭn type formula for canonical resolvents of dual pairs of linear relations”, Methods Funct. Anal. Topology, vol. 8, no. 4, pp. 72— 100, 2002.
8. T.V. Karataeva and V.D. Koshmanenko, “Generalized sum of operators”, Math. Notes, vol. 66, no. 5-6, pp. 556— 564, 2000.

References [transliteration]: 

1. S. Albeverio and P. Kurasov, “Singular perturbations of differential operators. Solvable Schrödinger type operators”, in London Math. Soc. Lecture Note Series, Cambridge: Cambridge University Press, 2000, vol. 271, xiv+429 pp.
2. S. Albeverio et al., Solvable models in quantum mechanics, 2nd ed., AMS Chelsea Publishing, Providence, RI, 2005, xiv+488 pp.
3. Koshmanenko V.D., Dudkin M.E. Metod osnashchenykh prostoriv u teoriï synhuli͡arnykh zburen′ samospri͡az͡henykh operatoriv. – K.: In-t matematyky NANU, 2013. – 320 s.
4. T. Kato and J.B. McLeod, “The functional-differential equation ”, Bull. Amer. Math. Soc., vol. 77, pp. 891–937, 1971.
5. V. Koshmanenko, Singular quadratic forms in perturbation theory (translated from the 1993 russian original by P.V. Malyshev and D.V. Malyshev), Mathematics and its Applications, vol. 474, pp. viii+308, 1999.
6. L.P. Nizhnik, “On rank one singular perturbations of selfadjoint operators”, Ibid, vol. 7, no. 3, pp. 54–66, 2001.
7. M.M. Malamud and V.I. Mogilevskii, “Kreĭn type formula for canonical resolvents of dual pairs of linear relations”, Methods Funct. Anal. Topology, vol. 8, no. 4, pp. 72–100, 2002.
3. T. V. Karataeva and V. D. Koshmanenko, “Generalized sum of operators”, Math. Notes, vol. 66, no. 5-6, pp. 556–564, 2000.

AttachmentSize
2014-4-2.pdf212.15 KB