FFT-like Multiplication of Linear Differential Operators

It is well known that integers or polynomials can be multiplied in an asymptotically fast way using the discrete Fourier transform. In this paper, we give an analogue of fast Fourier multiplication in the ring of skew polynomials C[ x, δ ], where δ = x . More precisely, we show that the multiplication problem of linear differential operators of degree n in x and degree n in δ can be reduced to the n × n matrix multiplication problem.