Decay estimates of functions through singular extensions of vector-valued Laplace transforms

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:375

Article

Martinez, Maria M.

关键词: Vector-valued Laplace transform;    C(0)-semigroups;    Rate of decay;   

DOI  :  10.1016/j.jmaa.2010.08.077

来源: Elsevier

【 摘 要 】

Let X be a Banach space and let f is an element of L(infinity)(R(+); X) whose Laplace transform extends analytically to some region containing iR \ {0}, possibly having a pole at the origin. In this paper, we give estimates of the decay of certain slight suitable modification of f in terms of the growth of its Laplace transform along the imaginary axis. This technique is applied to obtain decay estimates of smooth orbits of bounded C(0)-semigroups whose infinitesimal generators have an arbitrary finite boundary spectrum. These results are close to those given recently by C.J.K. Batty and T. Duyckaerts. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free