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B-splines of Blaschke product type
Chen Q.1; Qian T.2; Ren G.3; Wang Y.4
Source PublicationComputers and Mathematics with Applications

In this paper, we construct a class of new splines related to a Blaschke product. They emerge naturally when studying the filter functions of a class of linear time-invariant systems which are related to the boundary values of a Blaschke product for the purpose of sampling non-bandlimited signals using nonlinear Fourier atoms. The new splines generalize the well-known symmetric B-splines. We establish their properties such as integral representation property, a partition of unity property, a recurrence relation and difference property. We also investigate their random behaviour. Finally, our numerical experiments confirm our theories. 

KeywordB-spline Blaschke Product Central Limit Theorem Fourier Transform Sinc Function
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Indexed BySCI
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000297140300003
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Document TypeJournal article
Affiliation1.Cisco School of Informatics, Guangdong University of Foreign Studies, China
2.Department of Mathematics, University of Macau, Macau (Via Hong Kong)
3.Department of Mathematics, University of Science and Technology of China, Hefei, China
4.Department of Mathematics, Auburn University at Montgomery, P.O. Box 244023, Montgomery, AL 36124-4023, USA
Recommended Citation
GB/T 7714
Chen Q.,Qian T.,Ren G.,et al. B-splines of Blaschke product type[J]. Computers and Mathematics with Applications,2011,62(10):3669-3681.
APA Chen Q.,Qian T.,Ren G.,&Wang Y..(2011).B-splines of Blaschke product type.Computers and Mathematics with Applications,62(10),3669-3681.
MLA Chen Q.,et al."B-splines of Blaschke product type".Computers and Mathematics with Applications 62.10(2011):3669-3681.
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