Invertibility of convolution operators in problems of wave diffraction by a strip with reactance and Dirichlet conditions

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	Invertibility of convolution operators in problems of wave diffraction by a strip with reactance and Dirichlet conditions
	Castro, LP ; Zhang, B
	2005
发表期刊	ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN
ISSN	0232-2064
卷号	24 期号:3 页码:545-560
摘要	This paper deals with the invertibility of convolution type operators that come from a wave diffraction problem with reactance conditions on a strip. The diffraction problem is reformulated as a single convolution type operator on a finite interval. To develop an operator constructive approach, several matrix operator identities are established between this convolution type operator and certain new Wiener-Hopf operators, and certain equivalent properties are obtained between all the related operators. Factorizations are presented for particular semi-almost periodic matrix functions and the corresponding Wiener-Hopf operators. As a result, conditions are obtained to ensure the invertibility of all the convolution type operators associated with the problem. This leads to the well-posedness of the problem including the continuous dependence on the data. In obtaining our results a major role is played by the invertibility of the convolution type operator associated with the wave diffraction by a strip with equal Dirichlet conditions on both sides of the strip, which is obtained through an analytical representation. Both problems and the corresponding operators are considered in the framework of Bessel potential spaces.
关键词	convolution type operator wave diffraction Wiener-Hopf operator equivalence after extension relation
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000235282000006
出版者	HELDERMANN VERLAG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1168
专题	应用数学研究所
通讯作者	Castro, LP
作者单位	1.Univ Aveiro, Dept Math & Res Unit Matemat & Aplicacoes, P-3810193 Aveiro, Portugal 2.Coventry Univ, Sch Math & Informat Sci, Coventry CV1 5FB, W Midlands, England 3.Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Castro, LP,Zhang, B. Invertibility of convolution operators in problems of wave diffraction by a strip with reactance and Dirichlet conditions[J]. ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN,2005,24(3):545-560.
APA	Castro, LP,&Zhang, B.(2005).Invertibility of convolution operators in problems of wave diffraction by a strip with reactance and Dirichlet conditions.ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN,24(3),545-560.
MLA	Castro, LP,et al."Invertibility of convolution operators in problems of wave diffraction by a strip with reactance and Dirichlet conditions".ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN 24.3(2005):545-560.