Polynomial Frames: A Fast Tour

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A Quadrature Formula for Diffusion Polynomials Corresponding to a Generalized Heat Kernel (2010, methodology): “In [28, 24], we have developed a different multiscale analysis based on span {φk : `(2)k ≤ 2j} as the scaling spaces.”
Applications of classical approximation theory to periodic basis function networks and computational harmonic analysis (2013, methodology): “Using the same methods as in the trigonometric case and the above results, one can easily obtain direct and converse theorems as well as the wavelet-like representation theorems for characterization of suitably defined global smoothness classes; these results are formulated in [59].”
Diffusion polynomial frames on metric measure spaces (2008, methodology): “The frames are developed using a small variation of the ideas in [29], and a characterization of the Besov spaces is obtained using the frame transform.”