Wavelet thresholding estimator on interval via interpolatory Hermite splines

The convergence of wavelet series plays important roles in wavelet analysis. In particular, wavelet thresholding estimators for differential operators are discussed by many mathematicians. Great achievements have been made for the function space (Besov space) defined on the whole real line. Since a Besov space on interval is not a simply truncated one of that on the real line, this paper deals with wavelet thresholding estimators in Besov spaces on an interval. We firstly characterize those spaces by Hermite spline wavelets. Then we study the convergence of wavelet thresholding estimators on interval. It works because Hermite splines have interpolatory properties, or sampling properties in some sense.