Lp norm convergence of rational orthonormal basis function expansions

In this paper model sets for discrete-time LTI systems that are spanned by generalized orthonormal basis functions are investigated. It is established that the partial sums of Fourier series of generalized orthonormal basis expansions converge in all the spaces L^p and H^p, 1<p<∞. It is introduced a rational interpolation operator on nodes given on the unit circle. By using a generalization of the Marcinkiewicz classical L^p norm convergence theorems for trigonometric interpolation L ^p norm convergence is proved for the discrete rational operators, too