Laplace transforms of polynomially bounded vector-valued functions and semigroups of operators

被引：0
作者：
R. DeLaubenfels
Z. Huang
S. Wang
Y. Wang
机构：
[1] Ohio University,Mathematics Department
[2] Nanjing University,Mathematics Department
来源：
Israel Journal of Mathematics | 1997年 / 98卷
关键词：
Banach Space; Nonnegative Integer; Mild Solution; Closed Operator; Functional Calculus;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
For any natural numberk, we characterize once-integrated Laplace transforms ofO((1+t)k) andO(tk) Banach-space-valued functions. We use this to give Hille-Yosida type characterizations of generators of polynomially bounded strongly continuous semigroups, related families of operators, and solutions of the abstract Cauchy problem.
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页码：189 / 207
页数：18
相关论文
共 22 条
  • [1] Arendt W.(1987)Vector-valued Laplace transforms and Cauchy problems Israel Journal of Mathematics 59 327-353
  • [2] Balabane M.(1993)Spectral distributions and generalization of Stone's theorem to the Banach space Acta Applicandae Mathematicae 31 275-295
  • [3] Emamirad H.(1977)Strongly continuous semigroups, weak solutions, and the variation of constants formula Proceedings of the American Mathematical Society 63 370-373
  • [4] Jazar M.(1993)Unbounded holomorphic functional calculus and abstract Cauchy problems for operators with polynomially bounded resolvens Journal of Functional Analysis 114 348-394
  • [5] Ball J. M.(1993)Laplace and Laplace-Stieltjes spaces Journal of Functional Analysis 116 1-61
  • [6] deLaubenfels R.(1995)Regularized semigroups, existence families and the abstract Cauchy problem Journal of Differential and Integral Equations 8 1477-1496
  • [7] deLaubenfels R.(1993)On representations, inversions, and approximations of Laplace transforms in Banach spaces Applicable Analysis 49 151-170
  • [8] Kantorovitz S.(1992)Regularized semigroups and systems of linear partial differential equations Annali della Scuola Normale Superiore di Pisa 19 363-379
  • [9] deLaubenfels R.(1991)Integrated semigroups and differential operators on L Mathematische Annalen 291 1-16
  • [10] Sun G.(1988) spaces Journal of Mathematical Analysis and Applications 136 107-111
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