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Starting from the definition of an $n\times n$ $g$-Toeplitz matrix,$T_{n,g}(u)=\left[\widehat{u}_{r-gs}\right]_{r,s=0}^{n-1},$ where $g$ is agiven nonnegative parameter, $\{\widehat{u}_{k}\}$ is the sequence of Fouriercoefficients of the Lebesgue integrable function $u$ defined over the domain$\mathbb{T}=(-\pi,\pi]$, we consider the product of $g$-Toeplitz sequences ofmatrices, $\{T_{n,g}(f_{1})T_{n,g}(f_{2})\},$ which extends the product ofToeplitz structures, $\{T_{n}(f_{1})T_{n}(f_{2})\},$ in the case where thesymbols $f_{1},f_{2}\in L^{\infty}(\mathbb{T}).$ Under suitable assumptions,the spectral distribution in the eigenvalues sequence is completelycharacterized for the products of $g$-Toeplitz structures. Specifically, for$g\geq2$ our result shows that the sequences $\{T_{n,g}(f_{1})T_{n,g}(f_{2})\}$are clustered to zero. This extends the well-known result, which concerns theclassical case (that is, $g=1$) of products of Toeplitz matrices. Finally, alarge set of numerical examples confirming the theoretic analysis is presentedand discussed.

Spectral Distribution in the Eigenvalues Sequence of Products of g-Toeplitz Structures