
In a previous paper [Trans. Am. Math. Soc. 330, No. 2, 903-915 (1992; Zbl 0759.41009)] the authors have introduced the \(m\)th order cardinal \(B\)-spline-wavelet \(\psi_ m\) and have shown that every function \(f\in L^ 2(-\infty,\infty)\) has a (unique) orthogonal wavelet decomposition \(f=\sum_{k\in\mathbb{Z}}\sum_{j\in\mathbb{Z}}d^ k_ j\psi_ m(2^ k\cdot - j)\). The objective of the present paper is to analyze the wavelet series \(g_ k=\sum_{j\in\mathbb{Z}}d^ k_ j\psi_ m(2^ k\cdot -j)\). More precisely, the authors study the behaviour of the isolated sign changes of \(g_ k\) and, particularly, conditions under which the wavelet series \(g_ k\) is characterized by its isolated sign changes.
Mathematics(all), Numerical Analysis, Spline approximation, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), wavelet series, Applied Mathematics, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), cardinal \(B\)-spline-wavelet, Analysis
Mathematics(all), Numerical Analysis, Spline approximation, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), wavelet series, Applied Mathematics, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), cardinal \(B\)-spline-wavelet, Analysis
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