The ${\tau }_q$-Fourier transform: covariance and uniqueness

We propose an alternative definition for a Tsallis entropy composition-inspired Fourier transform, which we call “${\tau }_q$-Fourier transform”. We comment about the underlying “covariance” on the set of algebraic fields that motivates its introduction. We see that the definition of the ${\tau }_q$-Fourier transform is automatically invertible in the proper context. Based on recent results in Fourier analysis, it turns that the ${\tau }_q$-Fourier transform is essentially unique under the assumption of the exchange of the point-wise product of functions with their convolution.