A rough estimate for the spectral radius of the sampling operator. (Q1414694)

The author uses a Perron-Frobenius theorem due to \textit{H. Hennion} [Proc. Am. Math. Soc. 118, 627--634 (1993; Zbl 0772.60049)] for the spectral radius \(\widetilde\rho(S_\varphi)\) of \(S_\varphi | _{C({\mathbb T})}\) which states that \(\widetilde\rho(S_\varphi)=\lim_k\| S_\varphi 1\| _\infty^{1/k}\), provided that \(\varphi\geq0\) is continuous on the unit circle \(\mathbb T\). The spectral radius is computed in some nontrivial cases. Use is made of results in wavelet theory on the estimation of the regularity of interpolation schemes.