We study the asymptotic invertibility as \documentclass[12pt]{minimal}
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$$n \to+ \infty $$
\end{document} of matrices of the form \documentclass[12pt]{minimal}
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$$\alpha _{kj}^{(n)}= a(k/n,j/n,k - j)$$
\end{document} and \documentclass[12pt]{minimal}
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$$\beta _{kj}^{(n)}= b(k/E(n),j/E(n),k - j)$$
\end{document}, where a and b are functions defined on the sets \documentclass[12pt]{minimal}
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$$[0,1] \times [0,1] \times \mathbb{Z}{\text{ and [0, + }}\infty {\text{)}} \times {\text{[0, + }}\infty {\text{)}} \times \mathbb{Z}{\text{, respectively, }}E(n) \to+ \infty ,{\text{ and }}n/E(n) \to+ \infty $$
\end{document}. The joint asymptotic behavior of the spectrum of these matrices is analyzed.
