Non-convergence of the spherical harmonic expansion of gravitational potential below the Brillouin sphere: The continuous case

For a singleton planet, P, with gravitational potential, V, we show that for each ɛ > 0, there exists a planet P′ with gravitational potential V′, with (P′, V′) “ɛ-close” to (P, V) (in an appropriate C0-sense), for which the spherical harmonic expansion of V′ does not extend more than a distance...

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Veröffentlicht in:	Journal of mathematical physics 2021-10, Vol.62 (10)
Hauptverfasser:	Ogle, C., Costin, O., Bevis, M.
Format:	Artikel
Sprache:	eng
Schlagworte:	Physics Spherical harmonics
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description	For a singleton planet, P, with gravitational potential, V, we show that for each ɛ > 0, there exists a planet P′ with gravitational potential V′, with (P′, V′) “ɛ-close” to (P, V) (in an appropriate C0-sense), for which the spherical harmonic expansion of V′ does not extend more than a distance ɛ below the Brillouin sphere of P′.
doi_str_mv	10.1063/5.0044930
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subjects	Physics Spherical harmonics
title	Non-convergence of the spherical harmonic expansion of gravitational potential below the Brillouin sphere: The continuous case
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