论文标题
Khintchine类型定理用于仿射子空间
A Khintchine type theorem for affine subspaces
论文作者
论文摘要
我们表明，在某些乘法寄生虫条件下，欧几里得空间的仿射子空间是khintchine类型的分歧。这为猜想提供了证据，表明欧几里得空间的所有仿射子空间都是Khintchine类型的差异，或者Khintchine的定理在仅限于子空间时仍然存在。该结果被证明是更一般的Hausdorff度量结果的特殊情况，从中，还可以从中获得与适当子空间相交的W（τ）的Hausdorff尺寸。
We show that affine subspaces of Euclidean space are of Khintchine type for divergence under certain multiplicative Diophantine conditions on the parametrizing matrix. This provides evidence towards the conjecture that all affine subspaces of Euclidean space are of Khintchine type for divergence, or that Khintchine's theorem still holds when restricted to the subspace. This result is proved as a special case of a more general Hausdorff measure result from which the Hausdorff dimension of W(τ) intersected with an appropriate subspace is also obtained.
