论文标题
在polydisc和单位球中的随机插值序列
Random Interpolating Sequences in the Polydisc and the Unit Ball
论文作者
论文摘要
我们研究了在聚盘和单位球中随机序列的分离和插值特性。在单位球中，我们获得了0-1的Komolgorov定律，以使几乎所有Besov-sobolev空间$ b_ {2}^σ\ left（\ Mathbb {b} _ {d} _ {d} \ right）$ besov-sobolev空间进行插值。对于这些空间，由于挑选属性，这种插值序列与其乘数代数的插值序列一致。对于Hardy Space $ \ MATHRM {H}^2（\ Mathbb {D}^D）$及其乘数Algebra $ \ Mathrm { $ \ mathrm {h}^\ infty（\ mathbb {d}^d）$ - 几乎可以肯定。这两个条件不合时宜，因为确定性的起点的描述性较小，而不是单位球的对应物。另一方面，我们为$ \ mathrm {h}^2（\ Mathbb {d}^d）$的随机插值序列提供了$ 0-1 $ LAW。
We study almost sure separating and interpolating properties of random sequences in the polydisc and the unit ball. In the unit ball, we obtain the 0-1 Komolgorov law for a sequence to be interpolating almost surely for all the Besov-Sobolev spaces $B_{2}^σ\left(\mathbb{B}_{d}\right)$, in the range $0 < σ\leq1 / 2$. For those spaces, such interpolating sequences coincide with interpolating sequences for their multiplier algebras, thanks to the Pick property. This is not the case for the Hardy space $\mathrm{H}^2(\mathbb{D}^d)$ and its multiplier algebra $\mathrm{H}^\infty(\mathbb{D}^d)$: in the polydisc, we obtain a sufficient and a necessary condition for a sequence to be $\mathrm{H}^\infty(\mathbb{D}^d)$-interpolating almost surely. Those two conditions do not coincide, due to the fact that the deterministic starting point is less descriptive of interpolating sequences than its counterpart for the unit ball. On the other hand, we give the $0-1$ law for random interpolating sequences for $\mathrm{H}^2(\mathbb{D}^d)$.
