Convergence of the Cesàro mean for rational orthonormal bases

This paper deals with the convergence of the Cesàro mean for the rational orthonormal bases. Provided the set of zeroes of rational orthonormal bases is formed by a periodic repetition of the same finite sequence, the explicit expression of so-called block-Fejér kernel is available, and some properties of the block-Fejér kernel are discussed. Based on the convergence of the block-Cesàro mean, the convergence of Cesàro mean is also provided.