| 书目名称 | Vector-valued Laplace Transforms and Cauchy Problems | | 编辑 | Wolfgang Arendt,Charles J. K. Batty,Frank Neubrand | | 视频video | | | 丛书名称 | Monographs in Mathematics | | 图书封面 |  | | 描述 | Linear evolution equations in Banach spaces have seen important developments in the last two decades. This is due to the many different applications in the theory of partial differential equations, probability theory, mathematical physics, and other areas, and also to the development of new techniques. One important technique is given by the Laplace transform. It played an important role in the early development of semigroup theory, as can be seen in the pioneering monograph by Rille and Phillips [HP57]. But many new results and concepts have come from Laplace transform techniques in the last 15 years. In contrast to the classical theory, one particular feature of this method is that functions with values in a Banach space have to be considered. The aim of this book is to present the theory of linear evolution equations in a systematic way by using the methods of vector-valued Laplace transforms. It is simple to describe the basic idea relating these two subjects. Let A be a closed linear operator on a Banach space X. The Cauchy problern defined by A is the initial value problern (t 2 0), (CP) {u‘(t) = Au(t) u(O) = x, where x E X is a given initial value. If u is an exponentially b | | 出版日期 | Book 20011st edition | | 关键词 | Bochner integral; Evolution equations; Fourier transform; Laplace and Fourier transforms; differential e | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-5075-9 | | isbn_ebook | 978-3-0348-5075-9Series ISSN 1017-0480 Series E-ISSN 2296-4886 | | issn_series | 1017-0480 | | copyright | Birkhäuser Basel 2001 |
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发表于 2025-3-21 16:13:27
