An introduction to the theory of multipliers
An introduction to the theory of multipliers
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DOI：
10.1007/978-3-642-65030-7
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发表时间：
1971
期刊：
影响因子：
--
通讯作者：
R. Larsen
中科院分区：
文献类型：
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作者：
R. Larsen
当我第一次考虑写一本关于乘法器的书时，我的目的是制作一本中等大小的专着，涵盖整个理论，并且任何具有泛函和调和分析基础知识的人都可以访问和阅读。然而，我很快意识到这个目标无法实现。这种认识在《施普林格数学讲义》第 105 卷中出版的本著作初稿的序言中显而易见，并且在对编写本卷所需的手稿进行修订、扩展和修正之后，现在变得更加尖锐。因此，和以前一样，接下来几页中给出的处理是折衷的而不是确定的。主题的选择和呈现当然不是独一无二的，它既反映了我个人的喜好和不足，也反映了将本书限制在合理规模的必要性。在整个过程中，我特别强调了乘数表征问题的函数分析方面，并且通常只提出了该理论的交换版本。我还希望为读者提供了太多而不是太少的细节。
When I first considered writing a book about multipliers, it was my intention to produce a moderate sized monograph which covered the theory as a whole and which would be accessible and readable to anyone with a basic knowledge of functional and harmonic analysis. I soon realized, however, that such a goal could not be attained. This realization is apparent in the preface to the preliminary version of the present work which was published in the Springer Lecture Notes in Mathematics, Volume 105, and is even more acute now, after the revision, expansion and emendation of that manuscript needed to produce the present volume. Consequently, as before, the treatment given in the following pages is eclectric rather than definitive. The choice and presentation of the topics is certainly not unique, and reflects both my personal preferences and inadequacies, as well as the necessity of restricting the book to a reasonable size. Throughout I have given special emphasis to the func tional analytic aspects of the characterization problem for multipliers, and have, generally, only presented the commutative version of the theory. I have also, hopefully, provided too many details for the reader rather than too few.