Xiong Fu, Ying et Li, Luo Qing, Convergence of the Cesàro mean for rational orthonormal bases, Acta mathematica Sinica. English series (Print) , 25(4), 2009, pp. 581-592
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.