1997
DOI: 10.1007/bf02937334
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Laplace transforms of polynomially bounded vector-valued functions and semigroups of operators

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Cited by 13 publications
(9 citation statements)
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“…R. DeLaubenfels in [1] introduced the set Z(A, k) of all x in a Banach space X for which (1) has a mild solution such that (1 + t) −k u(t, x) is 267 uniformly continuous and bounded on R + = [0, ∞) for t , and investigated the maximal continuously embedded subspace, where a closed operator generates an O((1 +t) k ) strongly continuous semi-group. Motivated by [1], we consider the following second order abstract Cauchy problem…”
Section: Introduction and Main Resultsmentioning
confidence: 97%
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“…R. DeLaubenfels in [1] introduced the set Z(A, k) of all x in a Banach space X for which (1) has a mild solution such that (1 + t) −k u(t, x) is 267 uniformly continuous and bounded on R + = [0, ∞) for t , and investigated the maximal continuously embedded subspace, where a closed operator generates an O((1 +t) k ) strongly continuous semi-group. Motivated by [1], we consider the following second order abstract Cauchy problem…”
Section: Introduction and Main Resultsmentioning
confidence: 97%
“…Definition 4 [2] . Suppose ω : R + → R + \{0} satisfies the following conditions a) ω(0) = 1, ω(·) is continuous and increasing on…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…In [6,Chapter 5], [7], [8], [12] and [13], maximal continuously embedded subspaces, where a closed operator generates a bounded strongly continuous group, semigroup, or a Lipschitz continuous once-integrated semigroup, were constructed. In the following, we establish analogous constructions for strongly continuous semigroups and locally Lipschitz continuous once-integrated semigroups with growth ω .…”
Section: Theorem 38mentioning
confidence: 99%
“…Once-integrated Laplace transforms of vector-valued functions have been shown to be important for studying abstract Cauchy problems of the first and second order (see [1] and [7]). We restrict ourselves in this paper to the first order abstract Cauchy problem…”
Section: Introductionmentioning
confidence: 99%
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