EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 90(105), pp. 47–64 (2011)

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Marko Kostic

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

Abstract: The power $(-A)^b$, $b\in\Bbb{C}$ 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 (MSC2000): 47D06; 47D09, 47D60, 47D62, 47D99

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Electronic fulltext finalized on: 16 Nov 2011. This page was last modified: 30 Nov 2011.

© 2011 Mathematical Institute of the Serbian Academy of Science and Arts
© 2011 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition