Geodesic
Complex Powers of Nondensely Defined Operators
Publications de l'Institut Mathématique, _N_S_90 (2011) no. 104, p. 47 .

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The power $(-A)^b$, $bn\Bbb{C}$ is defined for a closed linear operator $A$ whose resolvent is polynomially bounded on the region which is, in general, strictly contained in an acute angle. It is proved that all structural properties of complex powers of densely defined operators with polynomially bounded resolvent remain true in the newly arisen situation. The fractional powers are considered as generators of analytic semigroups of growth order $r>0$ and applied in the study of corresponding incomplete abstract Cauchy problems. In the last section, the constructed powers are incorporated in the analysis of the existence and growth of mild solutions of operators generating fractionally integrated semigroups and cosine functions.
Classification : 47D06 47D09 47D60 47D62 47D99 
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     author = {Marko Kosti\'c},
     title = {Complex {Powers} of {Nondensely} {Defined} {Operators}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {47 },
     publisher = {mathdoc},
     volume = {_N_S_90},
     number = {104},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2011_N_S_90_104_a3/}
}
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Marko Kostić. Complex Powers of Nondensely Defined Operators. Publications de l'Institut Mathématique, _N_S_90 (2011) no. 104, p. 47 . http://geodesic.mathdoc.fr/item/PIM_2011_N_S_90_104_a3/