Geodesic
Negative powers of a singular Schrödinger operator and convergence of spectral decompositions
Matematičeskie zametki, Tome 59 (1996) no. 3, pp. 428-436 Cet article a éte moissonné depuis la source Math-Net.Ru

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We compare the $L_2(\mathbb R^N)$-norms of negative powers of various Laplace and Schrödinger operators possessing a singular potential whose singularities lie on some manifolds. We write out sufficient conditions for uniform convergence and localization of spectral decompositions of functions from the Liouville class. 
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     author = {A. R. Khalmukhamedov},
     title = {Negative powers of a~singular {Schr\"odinger} operator and convergence of spectral decompositions},
     journal = {Matemati\v{c}eskie zametki},
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     year = {1996},
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A. R. Khalmukhamedov. Negative powers of a singular Schrödinger operator and convergence of spectral decompositions. Matematičeskie zametki, Tome 59 (1996) no. 3, pp. 428-436. http://geodesic.mathdoc.fr/item/MZM_1996_59_3_a11/

[1] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, T. 2, Mir, M., 1978

[2] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969

[3] Ilin V. A., Moiseev E. I., “O spektralnykh razlozheniyakh, otvechayuschikh proizvolnomu neotritsatelnomu rasshireniyu obschego samosopryazhennogo ellipticheskogo operatora vtorogo poryadka”, Dokl. AN SSSR, 191:4 (1971), 770–772

[4] Alimov Sh. A., Khalmukhamedov A. R., Ravnomernaya summiruemost spektralnykh razlozhenii nepreryvnykh funktsii iz $L_2$. Uravneniya smeshannogo tipa i zadachi so svobodnoi granitsei, Fan, Tashkent, 1989

[5] Khalmukhamedov A. R., “O spektralnykh razlozheniyakh operatora Shredingera s potentsialom, singulyarnym na mnogoobraziyakh”, Matematicheskoe modelirovanie. Sovremennye problemy matematicheskoi fiziki i vychislitelnoi matematiki, Nauka, M., 1989, 294–300 | MR

[6] Metvalli A. A., Usloviya skhodimosti i summiruemosti spektralnykh razlozhenii, otvechayuschikh ellipticheskim operatoram, Diss. ... k. f.-m. n., Tashkent, 1991

[7] Khalmukhamedov A. R., Usloviya skhodimosti i lokalizatsii spektralnykh razlozhenii, otvechayuschikh ellipticheskim operatoram, Diss. ... k. f.-m. n., M., 1984 | Zbl

[8] Khermander L., “O srednikh Rissa spektralnykh funktsii ellipticheskikh differentsialnykh operatorov i sootvetstvuyuschikh spektralnykh razlozheniyakh”, Matematika, 12:5 (1968), 91–130

[9] Alimov Sh. A., “Ravnomernaya skhodimost i summiruemost spektralnykh razlozhenii funktsii iz $L_2^\alpha$”, Differents. uravneniya, 9:4 (1973), 669–681 | MR | Zbl