Stability and linear independence associated with wavelet decompositions

Jia, Rong Qing; Wang, Jianzhong

doi:10.1090/S0002-9939-1993-1120507-8

Stability and linear independence associated with wavelet decompositions
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by Rong Qing Jia and Jianzhong Wang

Proc. Amer. Math. Soc. 117 (1993), 1115-1124

DOI: https://doi.org/10.1090/S0002-9939-1993-1120507-8

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Abstract:

Wavelet decompositions are based on basis functions satisfying refinement equations. The stability, linear independence, and orthogonality of the integer translates of basis functions play an essential role in the study of wavelets. In this paper we characterize these properties in terms of the mask sequence in the refinement equation that the basis function satisfies.

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