Abstract
In 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.
Keywords
- Trigonometric Polynomial
- Previous Chapter
- Spectral Multiplicity
- Diagonal Measure
- Riesz Product
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© 2010 Springer-Verlag Berlin Heidelberg
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Queffélec, M. (2010). Spectral Multiplicity of General Automata. In: Substitution Dynamical Systems - Spectral Analysis. Lecture Notes in Mathematics(), vol 1294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11212-6_11
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DOI: https://doi.org/10.1007/978-3-642-11212-6_11
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11211-9
Online ISBN: 978-3-642-11212-6
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