## On the eigenstructure of the Bernstein kernel

Uri Itai

### Abstract

In approximation theory a common technique is to assume duality behavior between the Bernstein operator and the transformation matrix between the standard basis and the Bernstein basis. In this paper we shall produce an example that this assumption is not always correct. In particular, the eigenstructures of the operator and the transformation Matrix are distinguished.

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### Key words

eigenstructure, Bernstein operator, Bernstein polynomial basis

### AMS subject classifications

42C15, 42C30

 Vol. 37 (2010), pp. 105-112 Sofiya Ostrovska: On the approximation of analytic functions by the $q$-Bernstein polynomials in the case $q>1$