EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 87(101), pp. 9–37 (2010)

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Marko Kostic

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

Abstract: We systematically analyze regularization of different kinds of ultradistribution semigroups and sines, in general, with nondensely defined generators and contemplate several known results concerning the regularization of Gevrey type ultradistribution semigroups. We prove that, for every closed linear operator $A$ which generates an ultradistribution semigroup (sine), there exists a bounded injective operator $C$ such that $A$ generates a \emph{global differentiable} $C$-semigroup ($C$-cosine function) whose derivatives possess some expected properties of operator valued ultradifferentiable functions. With the help of regularized semigroups, we establish the new important characterizations of abstract Beurling spaces associated to nondensely defined generators of ultradistribution semigroups (sines). The study of regularization of ultradistribution sines also enables us to perceive significant ultradifferentiable properties of higher-order abstract Cauchy problems.

Classification (MSC2000): 47D06; 47D09, 47D60, 47D62, 47D99

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Electronic fulltext finalized on: 20 Apr 2010. This page was last modified: 14 May 2010.

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