126 research outputs found
On the Berg--Chen--Ismail theorem and the Nevanlinna-Pick problem
In 2002 C. Berg, Y. Chen, and M. Ismail found a nice relation between the
determinancy of the Hamburger moment problem and asymptotic behavior of the
smallest eigenvalues of the corresponding Hankel matrices. We investigate
whether an analog of this statement holds for the Nevanlinna--Pick
interpolation problem.Comment: 5 pages, LaTeX fil
Bernstein-type polynomials on several intervals
We construct the analogues of Bernstein polynomials on the set Js of s finitely many intervals. Two cases are considered: first when there are no restrictions on Js, and then when Js has a so-called T-polynomial. On such sets we define approximating operators resembling the classic Bernstein polynomials. Reproducing and interpolation properties as well as estimates for the rate of convergence are given. © Springer International Publishing AG 2017
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