EXTENDED RESOLVENTS AND EXTENDED SPECTRAL FUNCTIONS OF A HERMITIAN OPERATOR

EXTENDED RESOLVENTS AND EXTENDED SPECTRAL FUNCTIONS OF A HERMITIAN OPERATOR
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厄米算子的扩展分辨率和扩展谱函数

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发表时间：
1971
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通讯作者：
Ju. Šmul′jan
Ju. Šmul′jan
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文献类型：
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作者：
Ju. Šmul′jan

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本文构造了初始定义于希尔伯特空间流形上的厄米算子的扩展理论。操作符可能有无限的缺陷数，流形可能不致密。该扩展伴随着希尔伯特空间中理想元素（在属于基本希尔伯特空间的元素的希尔伯特空间上定义的广义函数）的结果。我们详细地分析了扩展广义分解和相应的谱函数。我们解释了形式的函数与-函数理论之间的联系，其中是一个扩展的广义解。参考书目：14篇。
In this paper we construct the theory of extensions of Hermitian operators which are initially defined on a manifold in Hilbert space. The operators may have infinite defect numbers, and the manifold may fail to be dense. The extension is accompanied by a result in the Hilbert space of ideal elements (generalized functions which are defined on the Hilbert space of elements which belong to the basic Hilbert space: ). We conduct a detailed analysis of extended generalized resolvents and corresponding spectral functions. We explain the connection between functions of the form , where is an extended generalized resolvent, and the theory of -functions.Bibliography: 14 titles.