The solvability and explicit solutions of two integral equations via generalized convolutions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:369

Article

Nguyen Minh Tuan¹  Nguyen Thi Thu Huyen² 

[1] Univ Hanoi, Dept Math Anal, Hanoi, Vietnam

[2] Univ Phuong Dong, Dept Math, Hanoi, Vietnam

关键词: Generalized convolution;    Hermite function;    Integral equation of convolution type;    Normed ring;   

DOI  :  10.1016/j.jmaa.2010.04.019

来源: Elsevier

【 摘 要 】

This paper presents the necessary and sufficient conditions for the solvability of two integral equations of convolution type: the first equation generalizes from integral equations with the Gaussian kernel, and the second one contains the Toeplitz plus Hankel kernels. Furthermore, the paper shows that the normed rings on L(1) (R(d)) are constructed by using the obtained convolutions, and an arbitrary Hermite function and appropriate linear combination of those functions are the weight-function of four generalized convolutions associating F and (F) over tilde. The open question about Hermitian weight-function of generalized convolution is posed at the end of the paper. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free