We show that, under suitable assumptions on the function a: [ 0 , 1 ]2× [ - π, π] → C, the sequence of variable-coefficient Toeplitz matrices generated by a is a generalized locally Toeplitz (GLT) sequence with symbol a(x, x, θ). This property, in combination with the theory of GLT sequences, allows us to derive a lot of spectral distribution (Szegő-type) results for various sequences of matrices, including those obtained from algebraic and non-algebraic operations on variable-coefficient Toeplitz sequences.
Spectral Distribution Results Beyond the Algebra Generated by Variable-Coefficient Toeplitz Sequences: The GLT Approach
Serra-Capizzano, Stefano
2018-01-01
Abstract
We show that, under suitable assumptions on the function a: [ 0 , 1 ]2× [ - π, π] → C, the sequence of variable-coefficient Toeplitz matrices generated by a is a generalized locally Toeplitz (GLT) sequence with symbol a(x, x, θ). This property, in combination with the theory of GLT sequences, allows us to derive a lot of spectral distribution (Szegő-type) results for various sequences of matrices, including those obtained from algebraic and non-algebraic operations on variable-coefficient Toeplitz sequences.
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