Orthogonal Non{Bandlimited Wavelets on the Sphere
نویسندگان
چکیده
This paper introduces orthogonal non{bandlimited wavelets on the sphere with respect to a certain Sobolev space topology. The construction of those kernels is based on a clustering of the index set N = f(n; k) 2 N0 Zj n k ng associated to the system of spherical harmonics fYn;kg(n;k)2N . The wavelets presented here form reproducing kernels of the spans of the clustered harmonics. More explicitly, the horizontal partition Mn = f(n; k) 2 Ng, n 2 N0 yields the usual Shannon wavelets, which are bandlimited, whereas non-bandlimited kernels can be obtained from a vertical clustering Bk = f(n; k); (n; k) 2 Ng, k 2 N0 . For this case a particular kernel is investigated in detail, and a wavelet representation is derived explicitly. AMS classi cation: Primary: 42C40, 65T60. Secondary: 86-08.
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