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Chen, Han-Lin

Spline wavelets on the unit circle. (English) Zbl 0877.65006

Result. Math. 31, No. 3-4, 322-336 (1997).
Spline function spaces over refined partitions form an excellent setting for multiresolution analysis which in turn leads to wavelet construction. The author considers complex spline function spaces defined on the unit circle with equispaced nodes and obtains an orthonormal basis in terms of the B-splines [cf. M. Kamada, K. Toraichi and R. Mori, J. Approximation Theory 55, No. 1, 27-34 (1988; Zbl 0679.41007)]. Two scale equations for such orthonormal bases are also derived. Thus a decomposition of the space of square integrable functions over \([0,2\pi]\) into different orthogonal subspaces is obtained. The decomposition and reconstruction formulas each consist of only two terms.
Reviewer: H.P.Dikshit (Bhopal)

Cited in 3 Documents

MSC:

65D07 Numerical computation using splines
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
30E10 Approximation in the complex plane
41A15 Spline approximation
65T60 Numerical methods for wavelets
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems

Keywords:

spline function spaces; spline wavelets; multiresolution analysis; orthonormal basis; decomposition; reconstruction

Citations:

Zbl 0679.41007
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Full Text: DOI

References:

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