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Backward shift invariant subspaces with applications to band preserving and phase retrieval problems
Tao Qian1; Lihui Tan2
2016-04-01
Source PublicationMathematical Methods in the Applied Sciences
ISSN10991476 01704214
Volume39Issue:6Pages:1591-1598
Abstract

The band preserving and phase retrieval problems have long been interested and studied. In this paper, we, for the first time, give solutions to these problems in terms of backward shift invariant subspaces. The backward shift method among other methods seems to be direct and natural. We show that a function g∈L(R),1≤p≤∞, with fg∈L(R), that makes the band of fg to be within that of f if and only if g divided by an inner function related to f, belongs to some backward shift invariant subspace in relation to f. By the construction of backward shift invariant space, the solution g is further explicitly represented through the span of the rational function system whose zeros are those of the Laplace transform of f. As an application, we also use the backward shift method to give a characterization for the solutions of the phase retrieval problem.

KeywordBackward Shift Invariant Subspace Band Preserving Laplace Transform Phase Retrieval
DOIhttp://doi.org/10.1002/mma.3591
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000373482100024
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorLihui Tan
Affiliation1.Faculty of Science and Technology, University of Macau, Taipa, Macau, China
2.School of Applied Mathematics, Guangdong University of Technology, Guangzhou, 510006 China
First Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Tao Qian,Lihui Tan. Backward shift invariant subspaces with applications to band preserving and phase retrieval problems[J]. Mathematical Methods in the Applied Sciences,2016,39(6):1591-1598.
APA Tao Qian,&Lihui Tan.(2016).Backward shift invariant subspaces with applications to band preserving and phase retrieval problems.Mathematical Methods in the Applied Sciences,39(6),1591-1598.
MLA Tao Qian,et al."Backward shift invariant subspaces with applications to band preserving and phase retrieval problems".Mathematical Methods in the Applied Sciences 39.6(2016):1591-1598.
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