Convolutions and integral equations weighted by multi-dimensional Hermite functions

被引：0
|
作者：
Castro, L. P. [1 ]
Guerra, R. C. [2 ]
Tuan, N. M. [3 ]
机构：
[1] Univ Aveiro, CIDMA Ctr Res & Dev Math & Applicat, Dept Math, P-3810193 Aveiro, Portugal
[2] Univ Coimbra, CMUC Ctr Math, Dept Math, Apartado 3008, P-3001501 Coimbra, Portugal
[3] Viet Nam Natl Univ, VNU Univ Educ, Dept Math, 144 Xuan Thuy Str, Hanoi, Vietnam
来源：
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS | 2022年 / 15卷 / 08期
关键词：
Convolution; Young's inequality; integral equation; Hermite function; normed ring; Wiener's algebra; SOLVABILITY; OPERATORS;
D O I：
10.1142/S1793557122501510
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the solvability of a very general class of integral equations whose kernel depends on four different functions. Necessary and sufficient conditions for the unique solvability of such integral equations are obtained. To achieve such a goal, the main technique consists in introducing eight new convolutions weighted by multi-dimensional Hermite functions and using them as convolutions somehow associated with our integral equations. In this way, two Young-type inequalities are also obtained.
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页数：35
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