Current Development in Theory and Applications of Wavelets
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Abstract: We
introduce the pseudo-Butterworth refinable function with order which
is defined by the pseudo-Butterworth masks
with positive integers n, mand nonnegative integer This family
contains pseudo-splines and
provides a rich family of refinable functions. The pseudo-Butterworth refinable
functions are not compactly supported but have
exponential decay to compensate for the lack of compact support. This paper
gives a comprehensive analysis of the pseudo-Butterworth refinable functions,
such as regularity, asymptotic analysis, approximation order, asymptotic
behavior as a parameter grows to the infinity and wavelet constructions, etc.,
comparable to the analysis of pseudo-splines of Dong and Shen [8] and to the
asymptotic behavior of Battle-Lemarie refinable function of Kim et al. [12].
