References
- Shannon C. A mathematical theory of communication. Bell System Technical Journal. 1948;27:379–423.
- Shannon C. Communication in the presence of noise. Proceedings of the IRE. 1949;37:10–21.
- Butzer PL, Engels W, Ries S. The Shannon sampling series and the reconstruction of signals in terms of linear, quadratic and cubic splines. SIAM Journal on Applied Mathematics. 1986;46:299–323.
- Chen Q, Micchelli CA, Wang Y. Functions with spline spectra and their applications. International Journal of Wavelets, Multiresolution and Information Processing. 2010;8(2):197–223.
- Chen Q, Qian T. Sampling theorem and multi-scale spectrum based on non-linear Fourier atoms. Applicable Analysis. 2009;88(6):903–19.
- Chen Q, Wang YB, Wang Y. A sampling theorem for non-bandlimited signals using generalized sinc functions. Computers & Mathematics with Applications. 2008;56:1650–61.
- Liu Z, Rao B. Characterization of polynomial decay rate for the solution of linear evolution equation. Zeitschrift Für Angewandte Mathematik und Physik [Journal of Applied Mathematics and Physics]. 2005;56:630–644.
- Phung KD. Polynomial decay rate for the dissipative wave equation. Journal of Differentiable Equations. 2007;240:92–124.
- Chen Q, Micchelli CA. The Bedrosian identity for functions analytic in a neighborhood of the unit circle. Complex Analysis and Operator Theory. 6(3): 781–798.
- Smale S, Zhou DX. Shannon sampling and function reconstruction from point values. Bulletin-American Mathematical Society. 2004;41:279–305.
- Aldroubi A, Leonetti C, Sun Q. Error analysis of frame reconstruction from noisy samples. IEEE Transactions on Signal Processing. 2008;56:2311–25.
- Daubechies I. Ten lectures on wavelets. Vol. 61 of CBMS. Philadelphia, PA: SIAM; 1992.
- Han B. Vector cascade algorithms and refinable function vectors in Sobolev spaces. Journal of Approximation Theory. 2003;24:693–714.
- Han B. Computing the smoothness exponent of a symmetric multivariate refinable function. SIAM Journal on Matrix Analysis and Applications. 2003;24:693–714.
- Han B. Construction of wavelets and framelets by the projection method. International Journal of Applied Mathematics. 2008;1:1–40.
- Li Y. Hermite-like interpolating refinable function vector and its application in signal recovering. Journal on Fourier Analysis and Applications. Online First. 2011. doi: 10.1007/s00041-011-9208-z
- Jiang QT. Matlab routines for Sobolev and Hölder smoothness computation of refinable functions. Technical report; 2001.