Abstract
AbstractIn the previous chapter, we made use of the bi-correlation matrix Z to get the maximal spectral type of the system (X ζ,T) associated with a primitive and aperiodic substitution of length q (and height equal to one). The diagonal measures λ j being q-strongly mixing, they must be equal or mutually singular and a better knowledge of the distinct ones is needed to estimate the spectral multiplicity of the system. However, the computation of Z is rather intricate and we begin by showing how to get these measures easily from the correlation matrix Σ = (σαβ). In the next section, we deduce the spectral multiplicity from Σ only and we close the chapter with examples.KeywordsTrigonometric PolynomialPrevious ChapterSpectral MultiplicityDiagonal MeasureRiesz ProductThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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