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Matrix Riesz Products

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

Abstract

Turning back to the correlation matrix Σ = (σαβ) associated, in the previous chapter, with the primitive and aperiodic substitution ζ of length q, we shall prove that Σ is the weak-star limit point of a product of matrices whose entries are trigonometric polynomials, in a way similar to the case of generalized Riesz products. This provides us with a constructive process to explicit Σ for special substitutions, such as commutative ones (Thue-Morse) but also for the Rudin-Shapiro substitution, and therefore, we will be able to deduce their maximal spectral type.

Keywords

  • Trigonometric Polynomial
  • Exceptional Sequence
  • Integral Sequence
  • Primitive Substitution
  • Pointwise Ergodic Theorem

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Correspondence to Martine Queffélec .

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© 2010 Springer-Verlag Berlin Heidelberg

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Queffélec, M. (2010). Matrix Riesz Products. 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_8

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