Spectral Measures

  • Giovanni BarbarinoEmail author
Part of the Springer INdAM Series book series (SINDAMS, volume 30)


The theory of spectral symbols links sequences of matrices with measurable functions expressing their asymptotic eigenvalue distributions. Usually, a sequence admits several spectral symbols, and it is not clear if a canonical one exists. Here we present a way to connect the sequences with the space of probability measure, so that each sequence admits a uniquely determined measure. The methods used are similar to those employed in the theory of generalized locally Toeplitz (GLT) sequences: a goal of this present contribution is in fact that of explaining how the two concepts are connected.


Probability measures Generalized locally Toeplitz sequences Complete pseudo-metrics Ergodic formula 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Scuola Normale SuperiorePisaItaly

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