Geodesic
Generalized Convolutions for the Fourier Integral Transforms and Applications
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 4, pp. 371-379

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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 $L^1(\mathbb R^d)$ are constructed, and the explicit solution in $L^1(\mathbb R^d)$ of the integral equations with the mixed Toeplitz–Hankel kernel are obtained.
Keywords: generalized convolution, normed ring, integral equation of convolution type. 
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Bui Thi Giang; Nguyen Minh Tuan. Generalized Convolutions for the Fourier Integral Transforms and Applications. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 4, pp. 371-379. http://geodesic.mathdoc.fr/item/JSFU_2008_1_4_a1/