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Characterization of biorthogonal cosine wavelets

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Abstract

This paper is devoted to the study of characterization of two-overlapping dual window functions that give rise to biorthogonal Schauder bases, frames, and Riesz bases by modulation of the cosines. We show that in this case any frame is a Riesz basis and our characterization of Riesz bases may be considered as a generalization of the theorems established by Coifman, et al. [6] and by Jawerth and Sweldens [9].

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Authors and Affiliations

  1. Center for Approximation Theory, Texas A&M University, 77843, College Station, TX

    Charles K. Chui & Xianliang Shi

Authors
  1. Charles K. Chui
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  2. Xianliang Shi
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Additional information

First named author: Research supported by NSF Grant #DMS-95-05460 and ARO Contract #DAAH 04-95-10193.

Second named author: Research supported by the Texas Higher Education Coordinating Board under Grant Numbers 999903-066, 999903-067, and 999903-109.

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Chui, C.K., Shi, X. Characterization of biorthogonal cosine wavelets. The Journal of Fourier Analysis and Applications 3, 559–575 (1997). https://doi.org/10.1007/BF02648884

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