A unified approach to scalar, vector, and tensor Slepian functions on the sphere and their construction by a commuting operator

被引：1

作者：

Michel, V ^{[1
]}

Plattner, A. ^{[2
]}

Seibert, K. ^{[1
]}

机构：

[1] Univ Siegen, Dept Math, Geomath Grp, Siegen, Germany

[2] Univ Alabama, Dept Geol Sci, Tuscaloosa, AL USA

来源：

ANALYSIS AND APPLICATIONS | 2022年 / 20卷 / 05期

关键词：

Commuting operator; constructive approximation; numerically efficient construction; Slepian functions; sphere; spherical harmonic; spin weight; tensorial functions; SPHEROIDAL WAVE-FUNCTIONS; HARMONICS;

D O I：

10.1142/S0219530521500317

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a unified approach for constructing Slepian functions - also known as prolate spheroidal wave functions - on the sphere for arbitrary tensor ranks including scalar, vectorial, and rank 2 tensorial Slepian functions, using spin-weighted spherical harmonics. For the special case of spherical cap regions, we derived commuting operators, allowing for a numerically stable and computationally efficient construction of the spin-weighted spherical-harmonic-based Slepian functions. Linear relationships between the spin-weighted and the classical scalar, vectorial, tensorial, and higher-rank spherical harmonics allow the construction of classical spherical-harmonic-based Slepian functions from their spin-weighted counterparts, effectively rendering the construction of spherical-cap Slepian functions for any tensorial rank a computationally fast and numerically stable task.

引用

页码：947 / 988

页数：42

共 46 条

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