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

Yeon Ju Lee and Jungho Yoon

Abstract and Applied Analysis, 2011, vol. 2011, 1-17

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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:593436

DOI: 10.1155/2011/593436

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