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The general complex case of the Bernstein-Nachbin approximation problem

S. Machado, Joao Bosco Prolla (1978)

Annales de l'institut Fourier

We present a solution to the (strict) Bernstein-Nachbin approximation problem in the general complex case. As a corollary, we get proofs of the analytic, the quasi-analytic, and the bounded criteria for localizability in the general complex case. This generalizes the known results of the real or self-adjoint complex cases, in the same way that Bishop’s Theorem generalizes the Weierstrass-Stone Theorem. However, even in the real or self-adjoint complex cases, the results that we obtain are stronger...

The sharpness of convergence results for q -Bernstein polynomials in the case q > 1

Sofiya Ostrovska (2008)

Czechoslovak Mathematical Journal

Due to the fact that in the case q > 1 the q -Bernstein polynomials are no longer positive linear operators on C [ 0 , 1 ] , the study of their convergence properties turns out to be essentially more difficult than that for q < 1 . In this paper, new saturation theorems related to the convergence of q -Bernstein polynomials in the case q > 1 are proved.

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