Journal of Fourier Analysis and Applications

, Volume 16, Issue 6, pp 885–900 | Cite as

Complex Wavelets and Framelets from Pseudo Splines



In this paper, we introduce complex pseudo splines that are derived from pseudo splines of type I. First, we show that the shifts of every complex pseudo spline are linearly independent. Therefore we can construct a biorthogonal wavelet system. Next, we investigate the Riesz basis property of the corresponding wavelet system generated by complex pseudo splines. The regularity of the complex pseudo splines will be analyzed. Furthermore, by using complex pseudo splines, we will construct symmetric or antisymmetric complex tight framelets with desired approximation order.


Complex pseudo splines Complex tight frame Complex Riesz wavelets Biorthogonal complex refinable function Dual frame 

Mathematics Subject Classification (2000)

42C40 42C05 41A25 


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Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhouP.R. China

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