The finite Hartley new convolutions and solvability of the integral equations with Toeplitz plus Hankel kernels

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:397

Article

Pham Ky Anh²  Nguyen Minh Tuan¹  Phan Duc Tuan³ 

[1] Viet Nam Natl Univ, Dept Math, Coll Educ, Hanoi, Vietnam

[2] Vietnam Natl Univ, Dept Comput & Appl Math, Coll Sci, Hanoi, Vietnam

[3] Univ Da Nang, Dept Math, Pedag Coll, Da Nang City, Vietnam

关键词: Generalized convolution;    Fourier series;    Hartley series;    Integral equation of convolution type;   

DOI  :  10.1016/j.jmaa.2012.07.041

来源: Elsevier

【 摘 要 】

The main aim of this work is to consider integral equations of convolution type with the Toeplitz plus Hankel kernels firstly posed by Tsitsiklis and Levy (1981) [11]. By constructing eight new generalized convolutions for the finite Hartley transforms we obtain a necessary and sufficient condition for the solvability and unique explicit L-2-solution of those equations. Thanks to this convolution approach the solvability condition obtained here is remarkably different from those in Tsitsiklis and Levy (1981)[11] and in other papers. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free