The Radon transform on a family of curves in the plane. II

Source abstract

A further discussion of Radon’s problem for curves in the plane given, for fixed ( p , ϕ ) (p,\phi ) , by r α cos ⁡ { α ( θ − ϕ ) } = p α {r^\alpha }\cos \{ \alpha (\theta - \phi )\} = {p^\alpha } . α \alpha real, α ≠ 0 \alpha \ne 0 . Functions yielding null transforms, and zeros of the Fourier components of the transforms are given for general α \alpha . and several orthogonal expansions are given for α = ± 1 / m \alpha = \pm 1/m . m = 1 , 2 , 3 … . m = 1,2,3 \ldots .