Spin-Weighted Spherical Harmonics and Their Application for the Construction of Tensor Slepian Functions on the Spherical Cap
Produktnummer:
18c3ae2e1875334b44b47092322ba99ae6
| Autor: | Seibert, Katrin |
|---|---|
| Themengebiete: | Christoffel-Darboux formula Kombinatorik und Graphentheorie Mathematik Shannon number Theoretische und mathematische Astronomie Wigner D- function spin-weighted Beltrami operator unified mathematical theory |
| Veröffentlichungsdatum: | 28.01.2019 |
| EAN: | 9783961820283 |
| Sprache: | Englisch |
| Seitenzahl: | 281 |
| Produktart: | Kartoniert / Broschiert |
| Verlag: | universi - Universitätsverlag Siegen |
Produktinformationen "Spin-Weighted Spherical Harmonics and Their Application for the Construction of Tensor Slepian Functions on the Spherical Cap"
The spin-weighted spherical harmonics of Newman and Penrose (1966) form an orthonormal basis of L2(O) on the unit sphere O and have a huge field of applications. We present a unified mathematical theory. Here, we not only collect already known properties in a mathematical way, but also show new ones as well. All of this is connected to the notation of the spherical harmonics. In addition, we use spin-weighted spherical harmonics to construct tensor Slepian functions on the sphere. Slepian functions are spatially concentrated and spectrally limited. Their concentration within a chosen region of the sphere allows for local inversions when only regional data are available, or enable the extraction of regional information. By using spin-weighted spherical harmonics, our theory offers several numerical advantages. Furthermore, we present a method for an efficient construction of tensor Slepian functions for spherical caps. In this context, we are able to construct a localized basis on the spherical cap for the cosmic microwave background (CMB) polarization.
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