Results on spline-Fourier and Ciesielski-Fourier series
Some recent results on spline-Fourier and Ciesielski-Fourier series are summarized. The convergence of spline Fourier series and the basis properties of the spline systems are considered. Some classical topics, that are well known for trigonometric and Walsh-Fourier series, are investigated for Ciesielski-Fourier series, such as inequalities for the Fourier coefficients, convergence a.e. and in norm, Fejér and $\theta$-summability, strong summability and multipliers. The connection between Fourier series and Hardy spaces is studied.