Revisiting the concentration problem of vector fields within a spherical\n cap: a commuting differential operator solution

2013/02/21 by Kornél Jahn, Jahn, Kornél, Nándor Bokor +1
Earth and Planetary Sciences · Economics, Econometrics and Finance · Engineering · Mathematics · Physics and Astronomy · #33C47 (Primary) #33F05 #34B24 #42C10 #47B32 (Secondary) #Advanced Thermodynamics and Statistical Mechanics #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Field-Flow Fractionation Techniques #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA) #Seismic Imaging and Inversion Techniques #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1302.5261

openalex publication_date 2013/02/21 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We propose a novel basis of vector functions, the mixed vector spherical\nharmonics that are closely related to the functions F_lm of Sheppard and\nT "or "ok and help us reduce the concentration problem of tangential vector\nfields within a spherical cap to an equivalent scalar problem. Exploiting an\nanalogy with previous results published by Gr "unbaum and his colleagues, we\nconstruct a differential operator that commutes with the concentration operator\nof this scalar problem and propose a stable and convenient method to obtain its\neigenfunctions. Having obtained the scalar eigenfunctions, the calculation of\ntangential vector Slepian functions is straightforward.\n

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