On the convolutions of Fourier-type transforms (Q651847)

The author introduces first generalized convolutions of the \(n\)-dimensional Fourier transform depending on two pairs \((A,a)\), \((B,b)\), where \(A\) and \(B\) are \(n\times n\) matrices and \(a\), \(b\) vectors of the \(n\)-dimensional Euclidean space. Then a convolution of the two-dimensional Fourier cosine transform and poly-convolutions of the one-dimensional Fourier cosine transform are considered and properties of the convolution are derived. An application on the solution of integral equations is added.