| The finite Hartley new convolutions and solvability of the integral equations with Toeplitz plus Hankel kernels |
| Tác giả hoặc Nhóm tác giả: Pham Ky Anh, Nguyen Minh Tuan, Phan Duc Tuan |
| Nơi đăng: Journal of Math. Analysis and Applications; Số: 397;Từ->đến trang: 537-549;Năm: 2013 |
| Lĩnh vực: Tự nhiên; Loại: Bài báo khoa học; Thể loại: Quốc tế |
| TÓM TẮT |
| 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 \cite{levy}. 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 \cite{levy} and in other papers. |
| ABSTRACT |
| 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 \cite{levy}. 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 \cite{levy} and in other papers. |
