Weighted Hermite-Fejér interpolation on the real line: L ∞ case

We give a weighted Hermite-Fejér-type interpolatory method on the real line, which is a positive operator on “good” matrices. We give an example on “good” interpolatory matrix by weighted Fekete points. To prove the convergence theorem we need the generalization of “Rodrigues’ property”. The present publication was written in the framework of the Hungarian-Spanish Scientific and Technological Governmental Cooperation, no. E-38/04, with the support of the Research and Technological Development Fund of Hungary and the Ministry of Education of Spain, and supported by Hungarian National Foundation for Scientific Research, Grant No. T049301.