Spectral Radius of the Sampling Operator with Continuous Symbol
نویسندگان
چکیده
Abstract. Let φ(θ) ∼ ∑∞ −∞ ake ikθ (where ak is the k-th Fourier coefficient of φ) be a bounded measurable function on the unit circle T. Consider the operator Sφ(m,n) on L2(T) whose matrix with respect to the standard basis { eikθ : k ∈ Z } is given by (ami−nj )i,j∈Z. In this paper, we give upper and lower bound estimation for r(Sφ(m,n)), the spectral radius of Sφ(m,n). Furthermore, we will show that in some cases (for example, if φ is continuous on
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