Displaying similar documents to “Rational approximation near zero sets of functions.”

Approximation on the sphere by Besov analytic functions

Evgueni Doubtsov (1997)

Studia Mathematica

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Boundary values of zero-smooth Besov analytic functions in the unit ball of ℂ n are investigated. Bounded Besov functions with prescribed lower semicontinuous modulus are constructed. Correction theorems for continuous Besov functions are proved. An approximation problem on great circles is studied.

Universal Taylor series

Vassili Nestoridis (1996)

Annales de l'institut Fourier

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We strengthen a result of Chui and Parnes and we prove that the set of universal Taylor series is a G δ -dense subset of the space of holomorphic functions defined in the open unit disc. Our result provides the answer to a question stated by S.K. Pichorides concerning the limit set of Taylor series. Moreover, we study some properties of universal Taylor series and show, in particular, that they are trigonometric series in the sense of D. Menchoff.