The eigenstructure of the Bernstein operator
The authors determine the eigenvalues and eigenfunctions of the Bernstein operator \(B_n\), the latter are, of course, \(n+1\) polynomials of degrees \(k=0,\dots,n\). They show that the \(k\)th eigen-polynomial \(p^{(n)}_k\) has \(k\) simple zeros in \([0,1]\) and describe \(\lim_{n\to\infty}p^{(n)}_k\), for fixed \(k\). Applications are given to iterates of the Bernstein operators, and to Bernstein quasi-interpolants.
eigenvalues and eigenfunctions of the Bernstein operators
scientific article; zbMATH DE number 1495767
scientific article