Generalized Convolutions for the Fourier Integral Transforms and Applications
Bui Thi Giang
Nguyen Minh Tuan
(Bui Thi Giang: Department of Basic Science Institute of Cryptography Science 141 Chien Thang Str., Hanoi Vietnam; Nguyen Minh Tuan: Department of Mathematical Analysis University of Hanoi 334 Nguyen Trai Str., Hanoi Vietnam, e-mail: firstname.lastname@example.org;)
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This paper provides some generalized convolutions for the Fourier integral transforms and treats the applications. Namely, there are six generalized convolutions with weight-function for the Fourier integral transforms. As for applications, the normed ring structures on L1(Rd) are constructed, and the explicit solution in L1(Rd) of the integral equations with the mixed Toeplitz-Hankel kernel are obtained.