论文标题
希尔伯特空间的奇异性方法
A Hilbert space approach to singularities of functions
论文作者
论文摘要
我们介绍了Hilbert Space $ \ Mathcal H $功能上$ω$的伪造的概念。粗略地，$ \ Mathcal H $的伪级式函数是将$ \ Mathcal H $ $ \ MATHCAL H $乘以$ \ MATHCAL H $的函数，我们允许在所有$ω$中定义假数的可能性。 $ \ Mathcal H $的伪型具有奇异性，该子空间包括$ \ MATHCAL H $，并概括了分析功能的奇异性概念，即使$ \ Mathcal H $的元素不需要享受任何类型的分析性。我们分析了这些奇异性的本质，并以功能理论术语对它们进行了广泛的分类。
We introduce the notion of a pseudomultiplier of a Hilbert space $\mathcal H$ of functions on a set $Ω$. Roughly, a pseudomultiplier of $\mathcal H$ is a function which multiplies a finite-codimensional subspace of $\mathcal H$ into $\mathcal H$, where we allow the possibility that a pseudomultiplier is not defined on all of $Ω$. A pseudomultiplier of $\mathcal H$ has singularities, which comprise a subspace of $\mathcal H$, and generalize the concept of singularities of an analytic function, even though the elements of $\mathcal H$ need not enjoy any sort of analyticity. We analyse the natures of these singularities, and obtain a broad classification of them in function-theoretic terms.
