Geodesic
Domains of fractional powers of ordinary differential operators in spaces $L_p$
Matematičeskie zametki, Tome 21 (1977) no. 4, pp. 509-518

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An exact description (in terms of smoothness and specified boundary conditions) is obtained for the domains of fractional powers of an ordinary differential operator of arbitrary order with general boundary conditions, acting in spaces $L_p$. 
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     author = {I. D. Evzerov},
     title = {Domains of fractional powers of ordinary differential operators in spaces $L_p$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {509--518},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_4_a7/}
}
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I. D. Evzerov. Domains of fractional powers of ordinary differential operators in spaces $L_p$. Matematičeskie zametki, Tome 21 (1977) no. 4, pp. 509-518. http://geodesic.mathdoc.fr/item/MZM_1977_21_4_a7/