Spectral measures

Giovanni Barbarino*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationStructured Matrices in Numerical Linear Algebra
Subtitle of host publicationAnalysis, Algorithms and Applications
Number of pages24
ISBN (Electronic)978-3-030-04088-8
Publication statusPublished - 2019
MoE publication typeA3 Part of a book or another research book

Publication series

NameSpringer INdAM Series
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198


  • Complete pseudo-metrics
  • Ergodic formula
  • Generalized locally toeplitz sequences
  • Probability measures


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