On the eigenstructure of the $(\alpha,q)$-Bernstein operator

TL;DR

This paper derives the eigenvalues and eigenvectors of the $(eta,q)$-Bernstein operator and analyzes their asymptotic behavior across all values of $q$, enhancing understanding of its spectral properties.

Contribution

It provides explicit eigenstructure and limit behavior of the $(eta,q)$-Bernstein operator, a novel spectral analysis in this context.

Findings

Eigenvalues and eigenvectors explicitly obtained

Limit behavior of eigenvalues and eigenvectors characterized

Spectral properties analyzed for all $q$ values

Abstract

We obtain eigenvalues and eigenvectors of the $(\alpha,q)$-Bernstein operator $T_{n,q,\alpha}$. Moreover, we will give the limit behaviour of these eigenvalues and eigenvectors for all $q.$