Multiresolution analysis and wavelets on \(S^ 2\) and \(S^ 3\). (English) Zbl 0849.42020
Summary: We construct a multiresolution analysis and a wavelet basis on two specific compact manifolds. Using special charts, the problem is reduced to finding appropriate nested spaces on rectangular domains. The claim of \(C^1\)-continuity gives rise to certain boundary conditions on the rectangles. To satisfy these conditions, we use a tensor product approach in which one factor is an exponential spline.
MSC:
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 41A15 | Spline approximation |
| 41A63 | Multidimensional problems |
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