ON EXCEPTIONAL SETS OF THE HILBERT TRANSFORM

Grigori A. Karagulyan

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ON EXCEPTIONAL SETS OF THE HILBERT TRANSFORM

机译：关于希尔伯特变换的例外集

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摘要

We prove several theorems concerning the exceptional sets of Hilbert transform on the real line. In particular, it is proved that any null set is exceptional set for the Hilbert transform of an indicator function. The paper also provides a real variable approach to the Kahane-Katsnelson theorem on divergence of Fourier series.

机译：我们证明了关于实线上希尔伯特变换的特殊集合的几个定理。特别地，证明了对于指示符函数的希尔伯特变换，任何空集都是例外集。本文还为傅里叶级数发散的Kahane-Katsnelson定理提供了一种实变量方法。

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来源
《Real analysis exchange》 |2017年第2期|311-328|共18页
作者
Grigori A. Karagulyan;
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作者单位

Faculty of Mathematics and Mechanics, Yerevan State University, Alex Manoogian, 1, 0025, Yerevan, Armenia;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Hilbert transform; exceptional null set; divergent Fourier series;

机译：希尔伯特变换特殊的空集;发散傅里叶级数;

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专利

1. Exceptional sets and Hilbert-Schmidt composition operators [J] . Gallardo-Gutierrez EA., Gonzalez MJ. Journal of Functional Analysis . 2003,第2期

机译：异常集和Hilbert-Schmidt复合运算符
2. Exceptional family of elements and the solvability of variational inequalities for unbounded sets in infinite dimensional Hilbert spaces [J] . Isac G., Zhao YB. Journal of Mathematical Analysis and Applications . 2000,第2期

机译：无限维希尔伯特空间中无穷集的超常元素族和变分不等式的可解性
3. The Hilbert Transform as an Iterated Fourier Transform: Comment ``The Hilbert Transform as an Iterated Laplace Transform'' [J] . Crystal Thomas H. Aerospace and Electronic Systems, IEEE Transactions on . 1968,第2期

机译：作为迭代傅立叶变换的希尔伯特变换：评论``作为迭代拉普拉斯变换的希尔伯特变换''
4. Classification of EEG data sets with Hilbert transform [C] . Mesut Şeker, Mehmet Siraç Özerdem Signal Processing and Communication Application Conference . 2016

机译：用希尔伯特变换对脑电数据集进行分类
5. Some contributions to analysis: A new space of generalized functions for integro-differential equations involving Hilbert transforms, and a note on the non-nuclearity of a space of test functions on Hilbert space. [D] . Donnelly, Roderick Kerry. 1988

机译：对分析的一些贡献：涉及Hilbert变换的积分微分方程的广义函数的新空间，以及关于Hilbert空间上测试函数的空间的非核性的注释。
6. Diagonalization of the finite Hilbert transform on two adjacent intervals: the Riemann–Hilbert approach [O] . Marco Bertola, Elliot Blackstone, Alexander Katsevich, -1

机译：有限Hilbert变换在两个相邻区间上的对角化：Riemann-Hilbert方法
7. On exceptional sets of Hilbert transform [O] . Karagulyan, Grigori 2016

机译：关于特殊的希尔伯特变换集
8. Inquiry: Effectiveness of the Complex Empirical Mode Decomposition Method, the Hilbert-Huang Transform, and the Fast-Fourier Transform for Analysis of Dynamic Objects [R] . Wallis, K. L. 2012

机译：查询：复杂经验模式分解方法，Hilbert-Huang变换和动态对象分析的快速傅里叶变换的有效性

ON EXCEPTIONAL SETS OF THE HILBERT TRANSFORM

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