The Fractional Hilbert Transform on the Real Line

被引：1

作者：

Abdullah, Naheed ^{[1
,2
]}

Iqbal, Saleem ^{[2
]}

Khalid, Asma ^{[3
]}

Al Johani, Amnah S. ^{[4
]}

Khan, Ilyas ^{[5
]}

Rehman, Abdul ^{[2
]}

Andualem, Mulugeta ^{[6
]}

机构：

[1] Govt Girls Post Grad Coll, Dept Math, Quetta, Pakistan

[2] Univ Balochistan, Dept Math, Quetta 87550, Pakistan

[3] SBK Womens Univ, Dept Math, Quetta 87300, Pakistan

[4] Univ Tabuk, Fac Sci, Math Dept, Tabuk, Saudi Arabia

[5] Majmaah Univ, Coll Sci Al Zulfi, Dept Math, POB 66, Majmaah 11952, Saudi Arabia

[6] Bonga Univ, Dept Math, Bonga, Ethiopia

来源：

MATHEMATICAL PROBLEMS IN ENGINEERING | 2022年 / 2022卷

关键词：

IMPLEMENTATION;

D O I：

10.1155/2022/5027907

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

This paper examines some special properties and important results of the fractional Hilbert transform (FHT) on the real line R. In this rigorous study, we modify certain theorems of classical Hilbert transform for FHT and develop new theorems. Moreover, FHT of some common functions is given and eigenfunctions are also studied. We prove that FHT, denoted by H-alpha, is an isomorphism on L-2 (R). We also show that in L-2 (R), FHT is an isometry. Furthermore, we investigate Riesz inequality on L-p (R) for p > 1 to establish Hilbert formulae for FHT.

引用

页数：11

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Iqbal, Saleem
Khalid, Asma
Al Johani, Amnah S.
Khan, Ilyas
Rehman, Abdul
Andualem, Mulugeta
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