Spin-Weighted Spherical Harmonics and Their Application for the Construction of Tensor Slepian Functions on the Spherical Cap
Seiten
2019
universi - Universitätsverlag Siegen
978-3-96182-028-3 (ISBN)
universi - Universitätsverlag Siegen
978-3-96182-028-3 (ISBN)
The spin-weighted spherical harmonics of Newman and Penrose (1966) form an orthonormal basis of L2(Ω) on the unit sphere Ω 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.
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.
| Erscheinungsdatum | 29.01.2019 |
|---|---|
| Zusatzinfo | Beinhaltet zahlreiche Farbgrafiken. |
| Verlagsort | Siegen |
| Sprache | englisch |
| Maße | 148 x 210 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Graphentheorie | |
| Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik | |
| Schlagworte | Christoffel-Darboux formula • Shannon number • spin-weighted Beltrami operator • unified mathematical theory • Wigner D- function |
| ISBN-10 | 3-96182-028-7 / 3961820287 |
| ISBN-13 | 978-3-96182-028-3 / 9783961820283 |
| Zustand | Neuware |
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Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
CHF 83,90
