On the Weber integral equation and solution to the Weber-Titchmarsh problem

被引：2
|
作者：
Yakubovich, S. [1 ]
机构：
[1] Univ Porto, Fac Sci, Dept Math, Rua Campo Alegre 687, P-4169007 Oporto, Portugal
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 460卷 / 01期
关键词：
Weber-Orr integral transforms; Mellin transform; Bessel functions; Associated Legendre functions;
D O I：
10.1016/j.jmaa.2017.12.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We derive sufficient conditions for the existence of the Weber formal solution of the corresponding integral equation, related to the familiar Weber-Orr integral transforms. This gives a solution to the old Weber-Titchmarsh problem (posed in [4]). Our method involves properties of the inverse Mellin transform of integrable functions. The Mellin-Parseval equality and some integrals with the associated Legendre functions are used. (C) 2017 Elsevier Inc. All rights reserved.
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页码：400 / 410
页数：11
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