The Bochner-convolution integral for generalized functional-valued functions of discrete-time normal martingales

doi:10.3906/mat-1912-21

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	The Bochner-convolution integral for generalized functional-valued functions of discrete-time normal martingales
	Chen Jinshu
刊名	TURKISH JOURNAL OF MATHEMATICS
	2020
卷号	44 期号:3 页码:698-711
关键词	Normal martingale Fubini theorem Bochner integral vector measure
ISSN号	1300-0098
DOI	10.3906/mat-1912-21
英文摘要	Let M be a discrete-time normal martingale satisfying some mild conditions, S(M) subset of L- (2) (M) subset of S* (M) be the Gel'fand triple constructed from the functionals of M. As is known, there is no usual multiplication in S* (M) since its elements are continuous linear functionals on S(M). However, by using the Fock transform, one can introduce convolution in S(M), which suggests that one can try to introduce a type of integral of an S(M)-valued function with respect to an S(M)-valued measure in the sense of convolution. In this paper, we just define such type of an integral. First, we introduce a class of S (M) -valued measures and examine their basic properties. Then, we define an integral of an S(M)-valued function with respect to an S(M)-valued measure and, among others, we establish a dominated convergence theorem for this integral. Finally, we also prove a Fubini type theorem for this integral.
WOS研究方向	Mathematics
语种	英语
出版者	SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK
WOS记录号	WOS:000532339300006
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/155269]
专题	理学院
作者单位	Lanzhou Univ Technol, Sch Sci, Lanzhou, Peoples R China
推荐引用方式 GB/T 7714	Chen Jinshu. The Bochner-convolution integral for generalized functional-valued functions of discrete-time normal martingales[J]. TURKISH JOURNAL OF MATHEMATICS,2020,44(3):698-711.
APA	Chen Jinshu.(2020).The Bochner-convolution integral for generalized functional-valued functions of discrete-time normal martingales.TURKISH JOURNAL OF MATHEMATICS,44(3),698-711.
MLA	Chen Jinshu."The Bochner-convolution integral for generalized functional-valued functions of discrete-time normal martingales".TURKISH JOURNAL OF MATHEMATICS 44.3(2020):698-711.