Szeg\H{o}-type theorems on compact Abelian groups and spectral approximations for multiplicative Toeplitz matrices
arxiv(2023)
摘要
We consider Szeg\H{o}-type theorems on compact Abelian groups. It is shown that for a large class of pairs $(\{\sigma_N\},\varphi)$, the sequence $\{(\det T_{\sigma_N}\varphi)^{1/\left|\sigma_N\right|}\}$ has at most two cluster points, and the sequence converges with a restriction of the growth of $\{\sigma_N\}$. By applying our results to the infinite torus $\mathbb{T}^\infty$, we give an affirmative answer to one problem and partly answer another problem posed by Nikolski and Pushnitski.
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