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

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.
http://www.springerlink.com/content/1069-5869
Approximating class of sequences; Eigenvalue distribution; Generalized convolution; Generalized locally Toeplitz sequence; Singular value distribution; Variable-coefficient Toeplitz matrix; Analysis; Mathematics (all); Applied Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11383/2073482
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