B-splines of Blaschke product type

Authors:
Qiuhui Chen;Tao Qian;Guangbin Ren;Yi Wang
Affiliations:
Cisco School of Informatics, Guangdong University of Foreign Studies, China;Department of Mathematics, University of Macau, Macau (Via Hong Kong);Department of Mathematics, University of Science and Technology of China, Hefei, China;Department of Mathematics, Auburn University at Montgomery, P.O. Box 244023, Montgomery, AL 36124-4023, USA
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

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.