Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines
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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.
2003 ◽
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pp. 75-92
2005 ◽
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pp. 67-77
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2005 ◽
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pp. 153-166
2008 ◽
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pp. 183-208
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2000 ◽
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pp. 153-170
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2008 ◽
Vol 151
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pp. 155-163
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