Geodesic
Regularization of Some Classes of Ultradistribution Semigroups and Sines
Publications de l'Institut Mathématique, _N_S_87 (2010) no. 101, p. 9 .

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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 : 47D06 47D09 47D60 47D62 47D99 
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     author = {Marko Kosti\'c},
     title = {Regularization of {Some} {Classes} of {Ultradistribution} {Semigroups} and {Sines}},
     journal = {Publications de l'Institut Math\'ematique},
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     number = {101},
     year = {2010},
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Marko Kostić. Regularization of Some Classes of Ultradistribution Semigroups and Sines. Publications de l'Institut Mathématique, _N_S_87 (2010) no. 101, p. 9 . http://geodesic.mathdoc.fr/item/PIM_2010_N_S_87_101_a1/