Hilbert Transform, Nevanlinna Class and Toeplitz Kernels

IF 0.7 4区数学 Q2 MATHEMATICS

Complex Analysis and Operator Theory Pub Date : 2024-04-07 DOI:10.1007/s11785-024-01521-5

Arun K. Bhardwaj, Javad Mashreghi, R. K. Srivastava

引用次数: 0

Abstract

In this article we obtain an explicit formula for the Hilbert transform of \(\log |f|,\) for the function f in Nevanlinna class having continuous extension to the real line. This family is the largest possible for which such a formula for the Hilbert transform of \(\log |f|,\) can be obtained. The formula is very general and implies several previously known results.

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希尔伯特变换、内万林纳类和托普利兹核

在这篇文章中，我们得到了在内万林那类中连续延伸到实线的函数 f 的 \(\log |f|,\) 的希尔伯特变换的明确公式。这个族是可以得到 \(\log |f|,\)的希尔伯特变换公式的最大族。这个公式非常通用，并隐含了几个之前已知的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Complex Analysis and Operator Theory 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

107

审稿时长

3 months

期刊介绍： Complex Analysis and Operator Theory (CAOT) is devoted to the publication of current research developments in the closely related fields of complex analysis and operator theory as well as in applications to system theory, harmonic analysis, probability, statistics, learning theory, mathematical physics and other related fields. Articles using the theory of reproducing kernel spaces are in particular welcomed.