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1.
Let Π n d denote the space of all spherical polynomials of degree at most n on the unit sphere $\mathbb{S}^{d}Let Π
n
d
denote the space of all spherical polynomials of degree at most n on the unit sphere
\mathbbSd\mathbb{S}^{d}
of ℝ
d+1, and let d(x,y) denote the geodesic distance arccos x⋅y between
x,y ? \mathbbSdx,y\in\mathbb{S}^{d}
. Given a spherical cap
B(e,a)={x ? \mathbbSd:d(x,e) £ a} (e ? \mathbbSd, a ? (0,p) is bounded awayfrom p),B(e,\alpha)=\big\{x\in\mathbb{S}^{d}:d(x,e)\leq\alpha\big\}\quad \bigl(e\in\mathbb{S}^{d},\ \alpha\in(0,\pi)\ \mbox{is bounded awayfrom}\ \pi\bigr), 相似文献
2.
V. M. Kaplitsky 《Journal of Mathematical Sciences》2010,165(4):455-462
We study sufficient conditions for exponential decay at infinity for eigenfunctions of a class of integral equations in unbounded
domains in ℝ
n
. We consider integral operators K whose kernels have the form
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