Generalized Convolutions for the Fourier Integral Transforms and Applications

Abstract

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.