In a recent paper [5] the fine
spectra of integer powers of the Cesàro matrix were computed. In this paper the fine
spectra of weighted mean methods are determined. In most cases investigated, the
interior points belong to III1, the boundary points, except 1, belong to II2, and 1 and
any isolated points belong to III3, where III1, II2, and III3 are portions of the state
space as described in [3].
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