Sheng Wang Wang, Mei Ying Wang, Yan Shen (2005)
Studia Mathematica
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Motivated by a great deal of interest in operators that may not be densely defined and do not generate global integrated semigroups, we establish general perturbation theorems for local integrated semigroups and describe their applications to local complete second order abstract differential equations.
Chung-Cheng Kuo (2010)
Studia Mathematica
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We apply the contraction mapping theorem to establish some bounded and unbounded perturbation theorems concerning nondegenerate local α-times integrated semigroups. Some unbounded perturbation results of Wang et al. [Studia Math. 170 (2005)] are also generalized. We also establish some growth properties of perturbations of local α-times integrated semigroups.
Miao Li, Fa-lun Huang, Quan Zheng (2001)
Studia Mathematica
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We introduce the notion of a local n-times integrated C-semigroup, which unifies the classes of local C-semigroups, local integrated semigroups and local C-cosine functions. We then study its relations to the C-wellposedness of the (n + 1)-times integrated Cauchy problem and second order abstract Cauchy problem. Finally, a generation theorem for local n-times integrated C-semigroups is given.
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.
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.
Miao Li, Quan Zheng (2003)
Studia Mathematica
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We investigate the relations between local α-times integrated semigroups and (α + 1)-times integrated Cauchy problems, and then the relations between global α-times integrated semigroups and regularized semigroups.
M. Zeitoun (1995)
Semigroup forum
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P.M. Higgins (1996)
Semigroup forum
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J. Gregory Dobbins (1976)
Mathematische Zeitschrift
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Tôru Saitô (1966)
Colloquium Mathematicae
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Karl-Hermann Neeb (1992)
Journal für die reine und angewandte Mathematik
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D.R. Brown, Rs.S. Houston (1986-1987)
Semigroup forum
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B. M. Schein (1974)
Colloquium Mathematicae
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Isabelle Chalendar, Jean Esterle, Jonathan R. Partington (2010)
Banach Center Publications
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The theory of quasimultipliers in Banach algebras is developed in order to provide a mechanism for defining the boundary values of analytic semigroups on a sector in the complex plane. Then, some methods are presented for deriving lower estimates for operators defined in terms of quasinilpotent semigroups using techniques from the theory of complex analysis.
M.V. Lawson (1989)
Semigroup forum
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J. P. Holmes (1974)
Colloquium Mathematicae
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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.