论文标题
Mandrekar定理的替代证明
Alternative proofs of Mandrekar's theorem
论文作者
论文摘要
我们提出了曼德卡（Mandrekar）定理的两个替代证明，该证明指出，比迪斯（Bidisc）上强烈空间的一个不变子空间准确地是在满足双重通勤条件时。第一个证明使用Toeplitz运算符的属性来得出某些移位不变子空间的复制核的公式，然后可以将其用于表征它们。第二个证明依赖于复制属性，以证明原点的复制内核必须生成整个变化不变的子空间。
We present two alternative proofs of Mandrekar's theorem, which states that an invariant subspaces of the Hardy space on the bidisc is of Beurling type precisely when the shifts satisfy a doubly commuting condition. The first proof uses properties of Toeplitz operators to derive a formula for the reproducing kernel of certain shift invariant subspaces, which can then be used to characterize them. The second proof relies on the reproducing property in order to show that the reproducing kernel at the origin must generate the entire shift invariant subspace.
