Một chập tổng quát cho Fourier, Fourier cosin và biến đổi sin được giới thiệu. Thuộc tính và các ứng dụng của nó đối với hệ thống giải quyết các phương trình nguyên được trình bày. | 33 4 2005 421-436 V í e t mi ai m J o u r mi ai l of MATHEMATICS ê VAST 2005 On the Generalized Convolution with a Weight - Function for Fourier Fourier Cosine and Sine Transforms Nguyen Xuan Thao1 and Nguyen Minh Khoa2 1 Hanoi Water Resources University 175 Tay Son Dong Da Hanoi Vietnam 2Hanoi Universtity of Transport and Communications Lang Thuong Dong Da Hanoi Vietnam Received December 15 2004 Revised July 2005 Abstract. A generalized convolution for Fourier Fourier cosine and sine transforms is introduced. Its properties and applications to solving systems of integral equations are presented. 1. Introduction . . . . .th . . . oo o 422 oo o oo c 0 c oo o 0 oo 0 oo . 1 . 0 1 423 1 . 2 . 3 . oo . - 2 . 2 2. Generalized Convolution for the Fourier Fourier Cosine and Sine Transforms Definition 1. Genneralized convolution with the weight-function. sign y for the Fourier Fourier cosine and sine transforms of functions f and g is defined by oo . . . . 0 o Denote by the set of all functions defined that 0 . Theorem 1. Let and be functions in . Then the genneralized convolution with the weight-function. sign for the Fourier Fourier cosine and sine transforms of functions and has a meaning and belongs to and the factorization property .
