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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.

Thin sequences in the corona of H ∞

Dimcho Stankov, Tzonio Tzonev (2013)

Open Mathematics

In this paper we consider several conditions for sequences of points in M(H ∞) and establish relations between them. We show that every interpolating sequence for QA of nontrivial points in the corona M ( H ) 𝔻 of H ∞ is a thin sequence for H ∞, which satisfies an additional topological condition. The discrete sequences in the Shilov boundary of H ∞ necessarily satisfy the same condition.

Traces and the F. and M. Riesz theorem for vector fields

Shiferaw Berhanu, Jorge Hounie (2003)

Annales de l’institut Fourier

This work studies conditions that insure the existence of weak boundary values for solutions of a complex, planar, smooth vector field L . Applications to the F. and M. Riesz property for vector fields are discussed.

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