Nonstationary Wavelets on the m - Spherefor Scattered
نویسندگان
چکیده
We construct classes of nonstationary wavelets generated by what we call spherical basis functions (SBFs), which comprise a subclass of Schoen-berg's positive deenite functions on the m-sphere. The wavelets are intrinsically deened 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 an uncertainty principle that expresses the trade-oo between localization and the presence of high harmonics|or high frequencies|in expansions in spherical harmonics. We discuss the application of this principle to the wavelets that we construct.
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