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Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines

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  • Yeon Ju Lee
  • Jungho Yoon

Abstract

This paper is concerned with analyzing the mathematical properties, such as the regularity and stability of nonstationary biorthogonal wavelet systems based on exponential B-splines. We first discuss the biorthogonality condition of the nonstationary refinable functions, and then we show that the refinable functions based on exponential B-splines have the same regularities as the ones based on the polynomial B-splines of the corresponding orders. In the context of nonstationary wavelets, the stability of wavelet bases is not implied by the stability of a refinable function. For this reason, we prove that the suggested nonstationary wavelets form Riesz bases for the space that they generate.

Suggested Citation

  • Yeon Ju Lee & Jungho Yoon, 2011. "Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-17, November.
    • Handle: RePEc:hin:jnlaaa:593436
    DOI: 10.1155/2011/593436
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