Abstract
In this paper, we construct a class of compactly supported wavelets by taking trigonometric B-splines as the scaling function. The duals of these wavelets are also constructed. With the help of these duals, we show that the collection of dilations and translations of such a wavelet forms a Riesz basis of 𝕃2(ℝ). Moreover, when a particular differential operator is applied to the wavelet, it also generates a Riesz basis for a particular generalized Sobolev space. Most of the proofs are based on three assumptions which are mild generalizations of three important lemmas of Jia et al. [Compactly supported wavelet bases for Sobolev spaces, Appl. Comput. Harmon. Anal. 15 (2003) 224–241].
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