Technical Report 2014-022

Tools for Determining the Asymptotic Spectral Distribution of Hermitian Matrix-Sequences and Applications

Carlo Garoni, Stefano Serra-Capizzano, and Paris Vassalos

December 2014

We consider sequences of Hermitian matrices with increasing dimension, and we provide a general tool for deducing the asymptotic spectral distribution of a `difficult' sequence {A<sub>n</sub>}<sub>n</sub>, starting from the one of `simpler' sequences {B_n,m}_n that approximate {A_n}_n when m→∞. The tool is based on the notion of approximating class of sequences (a.c.s.), which was inspired by the work of Paolo Tilli and the second author, and is applied here in a more general setting. An a.c.s.-based proof of the famous Szego theorem on the spectral distribution of Toeplitz matrices is finally presented.

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