论文标题
无界的维也纳 - hopf操作员和同构单数积分运算符
Unbounded Wiener-Hopf Operators and Isomorphic Singular Integral Operators
论文作者
论文摘要
提供了一些有关无界Wiener-HOPF操作员（WH）的一些预段和基本事实。 WH具有有理符号的详细研究，表明它们是密集定义的，并且具有有限的尺寸内核和缺陷空间。后一个空间以及域和范围明确确定。一个进一步的主题涉及半场wh。通过可封闭的操作员的乘积表达半曲调WH及其伴随，这种表示允许自然的自我参与扩展。结果表明，它与Friedrichs扩展相吻合。极性分解引起了希尔伯特空间同构的，该同构与基于希尔伯特转化的良好研究类型的奇异积分算子有关。
Some preliminaries and basic facts regarding unbounded Wiener-Hopf operators (WH) are provided. WH with rational symbols are studied in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains and ranges are explicitly determined. A further topic concerns semibounded WH. Expressing a semibounded WH by a product of a closable operator and its adjoint this representation allows for a natural self-adjoint extension. It is shown that it coincides with the Friedrichs extension. Polar decomposition gives rise to a Hilbert space isomorphism relating semibounded WH to singular integral operators of a well-studied type based on the Hilbert transformation.
