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

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
@article{10_2298_PIM0897015K,
     author = {Marko Kosti\'c},
     title = {Complex {Powers} of {Operators}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {15 },
     publisher = {mathdoc},
     volume = {_N_S_83},
     number = {97},
     year = {2008},
     doi = {10.2298/PIM0897015K},
     zbl = {1261.47024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0897015K/}
}
TY  - JOUR
AU  - Marko Kostić
TI  - Complex Powers of Operators
JO  - Publications de l'Institut Mathématique
PY  - 2008
SP  - 15 
VL  - _N_S_83
IS  - 97
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2298/PIM0897015K/
DO  - 10.2298/PIM0897015K
LA  - en
ID  - 10_2298_PIM0897015K
ER  - 
%0 Journal Article
%A Marko Kostić
%T Complex Powers of Operators
%J Publications de l'Institut Mathématique
%D 2008
%P 15 
%V _N_S_83
%N 97
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2298/PIM0897015K/
%R 10.2298/PIM0897015K
%G en
%F 10_2298_PIM0897015K
Marko Kostić. Complex Powers of Operators. Publications de l'Institut Mathématique, _N_S_83 (2008) no. 97, p. 15 . doi : 10.2298/PIM0897015K. http://geodesic.mathdoc.fr/articles/10.2298/PIM0897015K/

Cité par Sources :