Computing the Smoothness Exponent of a Symmetric Multivariate Refinable Function
SIAM Journal on Matrix Analysis and Applications
Quincunx fundamental refinable functions and Quincunx biorthogonal wavelets
Mathematics of Computation
Journal of Computational and Applied Mathematics - Special issue: Approximation theory, wavelets, and numerical analysis
Vector cascade algorithms and refinable function vectors in Sobolev spaces
Journal of Approximation Theory
Approximation with scaled shift-invariant spaces by means of quasi-projection operators
Journal of Approximation Theory
A sampling theorem for non-bandlimited signals using generalized Sinc functions
Computers & Mathematics with Applications
Generalized interpolating refinable function vectors
Journal of Computational and Applied Mathematics
Approximation by quasi-projection operators in Besov spaces
Journal of Approximation Theory
An Average Sampling Theorem for Bandlimited Stochastic Processes
IEEE Transactions on Information Theory
Bessel multiwavelet sequences and dual multiframelets in Sobolev spaces
Advances in Computational Mathematics
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Motivated by [B. Han, Z. Shen, Dual wavelet frames and Riesz bases in Sobolev spaces, Constr. Approx. 29 (2009) 369-406], we establish a sampling theorem in H^s(R^d), s1/2,d=1, using a special pair of dual frames. The converging rate of the corresponding sampling series is investigated, and then sampling approximation to a signal in Sobolev space is established. If a signal to be reconstructed satisfies a mild condition in Fourier transform, then its sampling series converges exponentially fast. As an application, the sampling approximation is used to modify interpolating error, which arises when using an interpolating refinable function to reconstruct f@?H^s(R^d), such that f can be arbitrarily approximated by its samples.