EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 83(97), pp. 15–25 (2008)

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Marko Kostic

Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia

Abstract: 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 $r>0$.

Classification (MSC2000): 47A99; 47D03; 47D09; 47D62

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Electronic fulltext finalized on: 21 Oct 2008. This page was last modified: 10 Dec 2008.

© 2008 Mathematical Institute of the Serbian Academy of Science and Arts
© 2008 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition