Geodesic
Negative powers of a~singular Schr\"odinger operator and convergence of spectral decompositions
Matematičeskie zametki, Tome 59 (1996) no. 3, pp. 428-436

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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. 
@article{MZM_1996_59_3_a11,
     author = {A. R. Khalmukhamedov},
     title = {Negative powers of a~singular {Schr\"odinger} operator and convergence of spectral decompositions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {428--436},
     publisher = {mathdoc},
     volume = {59},
     number = {3},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_3_a11/}
}
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A. R. Khalmukhamedov. Negative powers of a~singular Schr\"odinger 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/