Geodesic
Asymptotics of the spectrum of the Schrödinger operator with nonregular homogeneous potential
Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 19-37 
M. Z. Solomyak. Asymptotics of the spectrum of the Schrödinger operator with nonregular homogeneous potential. Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 19-37. http://geodesic.mathdoc.fr/item/SM_1986_55_1_a1/
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     title = {Asymptotics of the spectrum of the {Schr\"odinger} operator with nonregular homogeneous potential},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Formulas are proved for the spectral asymptotics of a multidimensional Schrödinger operator with potential which behaves nonregularly at infinity. Bibliography: 17 titles.

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[2] Rozenblyum G. V., “Raspredelenie diskretnogo spektra singulyarnykh differentsialnykh operatorov”, DAN SSSR, 202:5 (1972), 1012–1015

[3] Kostyuchenko A. G., Levitan B. M., “Ob asimptoticheskom povedenii sobstvennykh znachenii operatornoi zadachi Shturma–Liuvillya”, Funkts. analiz i ego prilozheniya, 1:1 (1967), 86–96 | MR | Zbl

[4] Aslanov G. I., Bairamogly M., “Asimptotika vzveshennogo sleda operatornogo uravneniya Shredingera”, Izv. AN AzerbSSR. Ser. fiz.-tekhn. i matem. nauk, 1977, no. 1, 46–51 | MR | Zbl

[5] Boimatov K. Kh., “Psevdodifferentsialnye operatory s operatornym simvolom”, DAN SSSR, 244:1 (1979), 20–23 | MR | Zbl

[6] Robert D., “Comprtement asymptotique des valeurs propres d'opérateurs du type Schrödinger a potentiel “dégénéré””, J. de Math, pures et appl., 61:3 (1982), 275–300 | MR | Zbl

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[8] Simon B., Nonclassical eigenvalue asymptotics, Preprint, 1983 | MR

[9] Birman M. Sh., Solomyak M. Z., “Spektralnaya asimptotika negladkikh ellipticheskikh operatorov”, Tr. MMO, 27 (1972), 3–52 | MR | Zbl

[10] Bylis I. L., Solomyak M. Z., “Spektralnaya asimptotika vyrozhdayuschikhsya ellipticheskikh operatorov”, DAN SSSR, 207:2 (1972), 262–265

[11] Fefferman Ch. L., “The uncertainty principle”, Bull. of The Amer. Math. Soc., 9:2 (1983), 129–206 | DOI | MR | Zbl

[12] Birman M. Sh., Solomyak M. Z., “Asimptotika spektra psevdodifferentsialnykh operatorov s anizotropno–odnorodnymi simvolami”, Vestn. LGU, 1977, no. 13, 13–21 | MR | Zbl

[13] Birman M. Sh., Solomyak M. Z., “Kolichestvennyi analiz v teoremakh vlozheniya Soboleva i prilozheniya k spektralnoi teorii”, Desyataya matem. shkola, Kiev, 1974, 5–189 | MR

[14] Rozenblyum G. V., “Raspredelenie diskretnogo spektra singulyarnykh differentsialnykh operatorov”, Izv. VUZov. Matematika, 1976, no. 1, 75–86 | Zbl

[15] Birman M. Sh., “O spektre singulyarnykh granichnykh zadach”, Matem. sb., 55(97) (1961), 125–174 | MR | Zbl

[16] Agmon S., “Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators”, Arch. Ration Mech. and Analysis, 28:3 (1968), 165–183 | MR | Zbl

[17] Solomyak M. Z., “Ob asimptotike spektra operatora Shredingera s neregulyarnym odnorodnym potentsialom”, DAN SSSR, 278:2 (1984), 291–295 | MR | Zbl