On Analog of Fourier Transform in Interior of the Light Cone

Abstract

We introduce an analog of Fourier transform ${\mathcal{F}}_h^{\rho }$ in interior of light cone that commutes with the action of the Lorentz group. We describe some properties of ${\mathcal{F}}_h^{\rho }$, namely, its action on pseudoradial functions and functions being products of pseudoradial function and space hyperbolic harmonics. We prove that ${\mathcal{F}}_h^{\rho }$-transform gives a one-to-one correspondence on each of the irreducible components of quasiregular representation. We calculate the inverse transform too.