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Hilbert–Pólya Operators in Krein Spaces
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2024-02-07 , DOI: 10.1134/s0037446624010087 V. V. Kapustin
中文翻译:
Kerin 空间中的希尔伯特-波利亚算子
更新日期:2024-02-08
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2024-02-07 , DOI: 10.1134/s0037446624010087 V. V. Kapustin
We construct some class of selfadjoint operators in the Krein spaces consisting of functions on the straight line \( \{\operatorname{Re}s=\frac{1}{2}\} \). Each of these operators is a rank-one perturbation of a selfadjoint operator in the corresponding Hilbert space and has eigenvalues complex numbers of the form \( \frac{1}{s(1-s)} \), where \( s \) ranges over the set of nontrivial zeros of the Riemann zeta-function.
中文翻译:
Kerin 空间中的希尔伯特-波利亚算子
我们在 Kerin 空间中构造了一类自共轭算子,由直线\( \{\operatorname{Re}s=\frac{1}{2}\} \)上的函数组成。这些算子中的每一个都是相应希尔伯特空间中自伴随算子的秩一扰动,并且具有形式为\( \frac{1}{s(1-s)} \)的特征值复数,其中\( s \ )范围涵盖黎曼 zeta 函数的非平凡零点集。