Norms of sampling operators Original Research Article

Let h(z) be an essentially bounded complex valued function on the unit circle image. Consider the corresponding Laurent operator image, where hn is the nth Fourier coefficient of h(z), image. Let us consider an operator Sh(p, q), which we shall call a sampling operator, defined as image, where image. These operators are obtained from Lh by “keeping” every qth column and every pth row in the bi-infinite matrix Lh. In our paper, we find an upper and lower bound for the norm of the operator Sh(p, q).