Equivalence between GLT sequences and measurable functions

Giovanni Barbarino

Research output: Contribution to journalArticleScientificpeer-review

20 Citations (Scopus)


The theory of Generalized Locally Toeplitz (GLT) sequences of matrices has been developed in order to study the asymptotic behaviour of particular spectral distributions when the dimension of the matrices tends to infinity. Key concepts in this theory are the notions of Approximating Classes of Sequences (a.c.s.) and spectral symbols that lead to defining a metric structure on the space of matrix sequences and provide a link with the measurable functions. In this paper we prove additional results regarding theoretical aspects, such as the completeness of the matrix sequences space with respect to the metric a.c.s. and the identification of the space of GLT sequences with the space of measurable functions.

Original languageEnglish
Pages (from-to)397-412
Number of pages16
JournalLinear Algebra and Its Applications
Publication statusPublished - 15 Sept 2017
MoE publication typeA1 Journal article-refereed


  • Approximating classes of sequences
  • Discretization of differential equations
  • Generalized locally Toeplitz sequences
  • Singular values and eigenvalues


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