Строго сингулярные возмущения ранга один несимметричным потенциалом

Рассматриваются построение и задача на собственные значения сильно сингулярно ранга один возмущенного самосопряженного оператора несимметричным потенциалом.

Год издания: 
2014
Номер: 
4
УДК: 
517.9
С. 13–16., Бібліогр.: 8 назв.
Литература: 

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.

Транслитерированый список литературы: 

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.

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