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Spectral Multiplicity of General Automata

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1294)

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

These 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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Correspondence to Martine Queffélec .

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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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