On Analog of Fourier Transform in Interior of the Light Cone

Abstract

We introduce an analog of Fourier transformFhρin interior of light cone that commutes with the action of the Lorentz group. We describe some properties ofFhρ, namely, its action on pseudoradial functions and functions being products of pseudoradial function and space hyperbolic harmonics. We prove thatFhρ-transform gives a one-to-one correspondence on each of the irreducible components of quasiregular representation. We calculate the inverse transform too.