Analysis of Compactly Supported Nonstationary BiorthogonalWavelet Systems Based on Exponential B‐Splines
Yeon Ju Lee, Jungho Yoon · Abstract and Applied Analysis · 2011
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.