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.
Spectral measures
Barbarino, Giovanni
2019
Abstract
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.File in questo prodotto:
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