• Korean Journal of Mathematics
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• 제7권2호
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• pp.219-226
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• 1999

In this paper, we discuss convergence theorem for exponentially bounded C-semigroups. We establish the convergence of the sequence of generators of exponentially bounded C-semigroups in some sense implies the convergence of the sequence of the corresponding exponentially bounded C-semigroups. Under the assumption that R(C) is dense, we show the equivalence between the convergence of generators and exponentially bounded C-semigroups.

• Korean Journal of Mathematics
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• 제9권2호
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• pp.115-121
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• 2001

In this paper, we establish the conditions that a mild C-existence family yields a solution to the abstract Cauchy problem. And we show the relation between mild C-existence family and C-regularized semigroup if the family of linear operators is exponentially bounded and C is a bounded injective linear operator.

• Korean Journal of Mathematics
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• 제6권1호
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• pp.9-15
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• 1998

In this paper, we show convergence and approximation theorem for C-semigroups. And we study the problem of approximation of an exponentially bounded C-semigroup on a Banach space X by a sequence of exponentially bounded C-semigroup on $X_n$.

• 호남수학학술지
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• 제26권4호
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• pp.401-409
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• 2004

In this paper, we show that C-resolvent of generator can be represented by Laplace transform and establish an exponential formula for C regularized semigroups whose antiderivatives are exponentially bounded.

• Korean Journal of Mathematics
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• 제12권2호
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• pp.165-169
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• 2004

In this paper, we establish an inversion formula for exponentially bounded C-regularized semigroup.

• 대한수학회보
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• 제26권1호
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• pp.53-67
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• 1989

• 대한수학회보
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• 제35권1호
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• pp.45-52
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• 1998

In this paper, we establish the exponential formula for C-semigroup. If A is the generator of a C-semigroup S(t), then S(t) can be represented by exp(tA) in some sense.