Characterization of the Fourier series of a distribution having a value at a point

Let f be a periodic distribution of period 2 pi. Let Sigma(n=-infinity)(infinity) a(n)e(in theta) be its Fourier series. We show that the distributional point value f(theta(0)) exists and equals gamma if and only if the partial sum Sigma(-x less than or equal to n less than or equal to ax) a(n)e(in theta 0)) converge to gamma in the Cesaro sense as x --> infinity for each a > 0.