Representation formulas for cosine and sine functions of operators.
Chun-San Lee, Sen-Yen Shaw (1985)
Aequationes mathematicae
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Chun-San Lee, Sen-Yen Shaw (1985)
Aequationes mathematicae
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Hisamitsu Serizawa (1992)
Aequationes mathematicae
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Adam Bobrowski, Wojciech Chojnacki (2013)
Studia Mathematica
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We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space 𝓛(X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family whose members are all scalar multiples of the identity operator. We also show that if the sets...
Sheng Wang Wang (2002)
Studia Mathematica
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Motivated by a great deal of interest recently in operators that may not be densely defined, we deal with regularized semigroups and integrated semigroups that are either not exponentially bounded or not defined on [0,∞) and generated by closed operators which may not be densely defined. Some characterizations and related examples are presented. Our results are extensions of the corresponding results produced by other authors.
S.Y. Shaw, Y.C. Li (1993)
Semigroup forum
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M. Kuczma (1964)
Annales Polonici Mathematici
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M. Kostić (2010)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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Pedro J. Miana (2005)
Studia Mathematica
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We introduce the notion of almost-distribution cosine functions in a setting similar to that of distribution semigroups defined by Lions. We prove general results on equivalence between almost-distribution cosine functions and α-times integrated cosine functions.
Marko Kostić, Stevan Pilipović (2007)
Kragujevac Journal of Mathematics
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V. A. Babalola, A. Olubummo (1974)
Colloquium Mathematicae
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deLaubenfels, Ralph, Lei, Yansong (1997)
Abstract and Applied Analysis
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Bálint Farkas (2004)
Studia Mathematica
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The notion of bi-continuous semigroups has recently been introduced to handle semigroups on Banach spaces that are only strongly continuous for a topology coarser than the norm-topology. In this paper, as a continuation of the systematic treatment of such semigroups started in [20-22], we provide a bounded perturbation theorem, which turns out to be quite general in view of various examples.
S.Y. Shaw, Y.C. Li (1993)
Semigroup forum
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N. Tanaka (1990)
Semigroup forum
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Elisabetta M. Mangino, Alfredo Peris (2011)
Studia Mathematica
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We study frequent hypercyclicity in the context of strongly continuous semigroups of operators. More precisely, we give a criterion (sufficient condition) for a semigroup to be frequently hypercyclic, whose formulation depends on the Pettis integral. This criterion can be verified in certain cases in terms of the infinitesimal generator of the semigroup. Applications are given for semigroups generated by Ornstein-Uhlenbeck operators, and especially for translation semigroups on weighted...
Naoki Tanaka (2003)
Studia Mathematica
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A class of perturbing operators for locally Lipschitz continuous integrated semigroups is introduced according to the idea of Miyadera. The paper gives perturbation theorems of Miyadera type for such integrated semigroups.