Turning back to the correlation matrix ∑ = (σ αβ) associated, in the previous chapter, with the primitive and aperiodic substitution ζ of length q, we shall prove that ∑ 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 ∑ 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. © 2010 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Queffélec, M. (2010). Matrix Riesz products. Lecture Notes in Mathematics, 1294, 209–224. https://doi.org/10.1007/978-3-642-11212-6_8
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