On a problem in radiotherapy: Questions of non‐negativity

A well‐known result is used to show that if g is a non‐negative function and the radiation field, f , is its Radon transform, the dose field, f̂, is the convolution of g with (1/π r ) and is necessarily non‐negative. Simple series expansions of f and f̂ are given, and the series for f is written as a finite Fourier series. Known properties of finite Fourier series are used to seek, fruitlessly, for useful conditions on the coefficients to ensure the non‐negativity of f .