Geodesic
Complex Powers of Operators
Publications de l'Institut Mathématique, _N_S_83 (2008) no. 97, p. 15

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We define the complex powers of a densely defined operator $A$ whose resolvent exists in a suitable region of the complex plane. Generally, this region is strictly contained in an angle and there exists $\alpha\in[0,\infty)$ such that the resolvent of $A$ is bounded by $O((1+|\lambda|)^\alpha)$ there. We prove that for some particular choices of a fractional number $b$, the negative of the fractional power $(-A)^b$ is the c.i.g. of an analytic semigroup of growth order $r>0$.
DOI : 10.2298/PIM0897015K
Classification : 47A99 47D03, 47D09, 47D62 
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     author = {Marko Kosti\'c},
     title = {Complex {Powers} of {Operators}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {15 },
     publisher = {mathdoc},
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Marko Kostić. Complex Powers of Operators. Publications de l'Institut Mathématique, _N_S_83 (2008) no. 97, p. 15 . doi: 10.2298/PIM0897015K

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