傅里叶正、余弦变换的加权卷积及其应用  

Weighted convolution of the Fourier sine-cosine transform and its application

作　　者：向仪 冯强[1] XIANG Yi;FENG Qiang(School of Mathematics and Computer Science,Yan'an University,Yan'an 716000,Shaanxi Province,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《浙江大学学报（理学版）》2023年第3期266-272,共7页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(62261055,61861044,62001193,11961072);陕西省自然科学基金资助项目(2022JM-400,2023-JC-YB-085).

摘　　要：傅里叶变换是求解积分方程常用的工具。基于傅里叶正弦变换与傅里叶余弦变换,定义了两类傅里叶混合加权卷积,得到了傅里叶正弦变换与傅里叶余弦变换的卷积定理,并研究了这两类卷积运算的性质及Young类不等式,将这两类混合加权卷积应用于求解卷积类积分方程,得到了卷积类积分方程的显式解。Fourier transform is a powerful tool often used to solve some integral equations.In this paper,two kinds of Fourier sine,cosine mixed weighted convolution are defined based on Fourier sine transform and Fourier cosine transform,the corresponding convolution theorems are obtained.The properties of these two kinds of mixed convolution operation and Young type inequality are also studied.And the explicit solutions of convolution type integral equations are obtained based on these two types of mixed weighted convolution.

关 键 词：傅里叶正-余弦变换 卷积定理 YOUNG不等式 积分方程 

分 类 号：O174.2[理学—数学]