The radon transform is an isomorphism between L2(Ba) and He(Za)

AbstractIt is proved that the radon transform R is an isomorphism between X := L2(Ba) and Y := He(Za), where Ba is the ball of radius a centered at the origin in Rn, n≥2 and Za := Sn−1 × [−a,a], Sn−1 is the unit sphere in Rn, and He(Za) is the space of even functions g(α,p) which vanish at p = ±a, satisfy the moment conditions, and have finite norm ∫Sn−1∫−∞∞|Fg|(1+λ2)(n-1)2dλdα12 ≔ |g| ⩽ ∞)