On some operator colligations and associated reproducing kernel Pontryagin spaces
On some operator colligations and associated reproducing kernel Pontryagin spaces
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关于一些算子排序和关联的再生内核 Pontryagin 空间
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
H. Snoo
中科院分区：
文献类型：
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作者：
D. Alpay;V. Bolotnikov;A. Dijksma;H. Snoo
设s为舒尔函数，即单位圆盘d上的解析压缩函数，则函数1 -s(z) s()*/1 -z *在D. L. de Branges和J. Rovnyak中是正的，证明了相关的再现核希尔伯特空间为s的共等长实现提供了空间。在之前的工作中，我们将这一结果推广到以1-z *代替分母为a(z) a()* -b(z) b()*的算子值函数的情况。其中a和b是满足一定条件的解析函数。在本工作中，我们去掉了正条件，允许核函数有若干个负平方。此外，我们考虑函数的值是具有相同索引的庞特里亚金空间之间的有界算子。我们证明存在再现核庞特里亚金空间，它提供了函数的幺正、等距和共等距实现。我们还研究了上述核的投影版本。(C) 1996学术出版社，Inc.
Let s be a Schur function, that is a function analytic and contractive in the unit disk D. Then the function 1 -s(z) s(omega)*/1 -z omega* is positive in D. L. de Branges and J. Rovnyak proved that the associated reproducing kernel Hilbert space provides the stare space for a coisometric realization of s. In a previous work we extended this result to the case of operator valued functions with the denominator 1-z omega* replaced by a(z) a(omega)* -b(z) b(omega)*, where a and b are analytic functions subject to some conditions. In the present work we remove the positivity condition and allow the kernel to have a number of negative squares. Moreover, we consider functions whose values are bounded operators between Pontryagin spaces with the same index. We show that there exist reproducing kernel Pontryagin spaces which provide unitary, isometric, and coisometric realizations of the function. We also study the projective version of the above kernel. (C) 1996 Academic Press, Inc.