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Integral spline wavelet transform and its approximation properties. (Chinese. English summary) Zbl 0991.42020

This paper proves the trivial result that the \(r\)th-order polynomial spline wavelet \(\psi_r(x)\) satisfies the admissible condition \(\int {|\widehat \psi_r(\xi)|^2 \over |\xi|} d\xi<+\infty\), thus the corresponding continuous wavelet transform with wavelet \(\psi_r(x)\) does exist. The so-called approximation properties have not been given in this paper.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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