论文标题
在布里鲁因球体下方的重力电位的球形谐波扩展的不连贯；连续的情况
Non-convergence of the spherical harmonic expansion of gravitational potential below the Brillouin sphere; the continuous case
论文作者
论文摘要
对于带有引力潜力$ v $的单胎星球$ p $，我们表明，对于每个$ \ varepsilon> 0 $，存在一个带有引力潜在$ v'$的星球$ p'$，带有$（p'，v'）$“ $ \ varepsilon $ -close $ -close -close -close $ close” to $（p，p，v）$（$ c^0 $ c^0 $ c^0 $ c^0 $ c^0 $ c^0 $ c^0 $ c^0 $ c^0 $ c^0 $ c^0 $ c^0 $ c^0 $ p'$以下的距离$ \ varepsilon $。
For a singleton planet $P$ with gravitational potential $V$, we show that for each $\varepsilon > 0$ there exists a planet $P'$ with gravitational potential $V'$, with $(P',V')$ "$\varepsilon$-close" to $(P,V)$ (in an appropriate $C^0$-sense) for which the spherical harmonic expansion of $V'$ does not extend more than a distance $\varepsilon$ below the Brillouin sphere of $P'$.
