Mandrekar定理的另一种证明
Alternative proofs of Mandrekar's theorem
摘要：
本文给出了Mandrekar定理的两种不同的证明，该定理指出当移位满足双交换条件时，双圆盘上Hardy空间的一个不变子空间是Beurling型的.第一个证明利用Toeplitz算子的性质导出了某些移位不变子空间的再生核的公式，然后可以用它来刻画它们。第二个证明依赖于再生性质，以表明在原点的再生核必须生成整个移位不变子空间。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
