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- W4302327562 abstract "We propose a novel basis of vector functions, the mixed vector spherical harmonics that are closely related to the functions $F_{lm}$ of Sheppard and Torok and help us reduce the concentration problem of tangential vector fields within a spherical cap to an equivalent scalar problem. Exploiting an analogy with previous results published by Grunbaum and his colleagues, we construct a differential operator that commutes with the concentration operator of this scalar problem and propose a stable and convenient method to obtain its eigenfunctions. Having obtained the scalar eigenfunctions, the calculation of tangential vector Slepian functions is straightforward." @default.
- W4302327562 created "2022-10-06" @default.
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- W4302327562 date "2013-02-21" @default.
- W4302327562 modified "2023-09-23" @default.
- W4302327562 title "Revisiting the concentration problem of vector fields within a spherical cap: a commuting differential operator solution" @default.
- W4302327562 doi "https://doi.org/10.48550/arxiv.1302.5261" @default.
- W4302327562 hasPublicationYear "2013" @default.
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