7.—Convolution of Vector Measures
7.—Convolution of Vector Measures
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7.—矢量测量的卷积
DOI：
10.1017/s0308210500016322
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发表时间：
1975
期刊：
影响因子：
--
通讯作者：
A. J. White
中科院分区：
文献类型：
--
作者：
A. J. White
在本文中，我们考虑的问题，定义卷积，类似于经典的卷积的标量措施，措施上定义的Borel集的局部紧半群S和值的Banach代数。使用bilinearintegral介绍巴特尔，我们表明，形式主义的标量情况下坚持相当普遍的情况下，使公式适当的解释，给出了一个Banach代数结构的一大类值的措施定义在S。这些方法利用了向量测度和算子之间的联系，并涉及到一些独立的结果。
Synopsis In this paper we consider the problem of defining a convolution, analogous to the classical convolution of scalar measures, of measures defined on the Borel sets of a locally compact semi-group S and having values in a Banach algebra . Using the bilinearintegral introduced by Bartle we show that the formalism of the scalar case persists in situations of considerable generality so that the formula suitably interpreted, gives a Banach algebra structure to a large class of valued measures defined on S. Themethods exploit the connection between vector measures and operators and involve some results of independent interest.