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Abstract: We construct classes of nonstationary wavelets generated by what we call spherical basis functions (SBFs), which comprise a subclass of Schoenberg 's positive definite functions on the m-sphere. The wavelets are intrinsically defined on the m-sphere, and are independent of the choice of coordinate system. In addition, they may be orthogonalized easily, if desired. We will discuss decomposition, reconstruction, and localization for these wavelets. In the special case of the 2-sphere, we derive... (Update)
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...4, the localization properties of the orthogonalized functions are considered. Finally, let us remark that recently, Narcowich and Ward [11,12] also studied wavelets and localization properties on higher dimensional spheres, while asymptotically optimal results for compactly...
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2: Multivariate interpolation and conditionally positive definite functions (context) - Madych, Nelson - 1988
BibTeX entry: (Update)
F. J. Narcowich and J. D. Ward, Non-stationary wavelets on the m-sphere for scattered data, Appl. Comput. Harmonic Anal. 3 (1996), 324--336. http://citeseer.ist.psu.edu/narcowich96nonstationary.html More
@misc{ narcowich96nonstationary,
author = "F. Narcowich and J. Ward",
title = "Non-stationary wavelets on the m-sphere for scattered data",
text = "F. J. Narcowich and J. D. Ward, Non-stationary wavelets on the m-sphere
for scattered data, Appl. Comput. Harmonic Anal. 3 (1996), 324--336.",
year = "1996",
url = "citeseer.ist.psu.edu/narcowich96nonstationary.html" }
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20 Wavelets Associated with Periodic Basis Functions - Narcowich, Ward
18 Spherical Harmonics (context) - Muller - 1966
17 Trigonometric Interpolation and Wavelet Decomposition - Prestin, Quak - 1993
16 Spherical Wavelet Transform and its Discretization (context) - Freeden, Windheuser - 1995
16 Generalized Hermite Interpolation and Positive Definite Kern.. (context) - Narcowich - 1995
15 Periodic Orthogonal Splines and Wavelets (context) - Koh, Lee et al.
15 Quantum Mechanics (context) - Merzbacher - 1961
15 Theory of Bessel Functions (context) - Watson - 1966
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10 Strictly Positive Definite Functions on Spheres (context) - Xu, Cheney - 1992
10 Embeddings and Extensions in Analysis (context) - Wells, Williams - 1975
10 Differential and Integral Calculus (context) - Courant - 1936
9 On Spherical Spline Interpolation and Approximation (context) - Freeden - 1981
6 Wavelets for analyzing scattered data: an unbounded operator.. (context) - Chui, Jetter et al. - 1994
6 Strictly Positive Definite Functions on Spheres (context) - Ron, Sun
4 Fundamental sets of continuous functions on spheres (context) - Sun, Cheney - 1994
4 The Functions of Mathematical Physics (context) - Hochstadt - 1971
3 Continuous wavelet transforms on the sphere (context) - Holschneider
3 The theory of radial basis approximation (context) - Powell - 1990
3 Tensor spherical harmonics and tensor spherical splines - Freeden, Gervens et al. - 1994
2 Nonstationary spherical wavelets for scattered data (context) - Narcowich, Ward - 1995
2 Periodic spline wavelets (context) - Plonka, Tasche - 1993
2 Commentary on a Footnote (context) - Askey - 1988
1 Interpolating Wavelets on [\Gamma1; 1] and the Sphere (context) - Tasche - 1995
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