Geodesic
On fractional powers of the Schr\"odinger operator with a potential singular on manifolds
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2023), pp. 11-19

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Sufficient conditions on the degree of summability $p$ are found under which the Sсhrödinger operator with a potential singular on manifolds is a positive operator in Banach spaces $L_p$, and it is also shown that the domains of different degrees of this operator form an interpolation pair. In addition, we establish sufficient conditions on $p$ that ensure that fractional powers $\sigma$, $0 \sigma 1$ of the operator are bounded from $W_p^{2\sigma}$ to $L_p$.
Keywords: Fractional power, the Schrödinger operator, positive operator, Banach space. 
@article{IVM_2023_5_a1,
     author = {T. N. Alikulov and A. R. Khalmukhamedov},
     title = {On fractional powers of the {Schr\"odinger} operator with a potential singular on manifolds},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {11--19},
     publisher = {mathdoc},
     number = {5},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_5_a1/}
}
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T. N. Alikulov; A. R. Khalmukhamedov. On fractional powers of the Schr\"odinger operator with a potential singular on manifolds. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2023), pp. 11-19. http://geodesic.mathdoc.fr/item/IVM_2023_5_a1/