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作者:Wolfgang Gehlen
来源:[J].Complex Variables and Elliptic Equations(IF 0.5), 1996, Vol.29 (4), pp.379-382Taylor & Francis
摘要:In this note we deal with the limit points of zeros of the sections of a power series. The sharpness of Jentzsch's theorem is analysed by constructing a power series with the property that certain subsequences of its partial sums have prescribed sets as their sets of limit points...
作者:Wolfgang Gehlen , Wolfgang Luh , Jurgen Muller
来源:[J].Complex Variables and Elliptic Equations(IF 0.5), 2000, Vol.41 (1), pp.81-90Taylor & Francis
摘要:In this article we consider functions φ which are holomorphic exactly on a domain [image omitted] and whose power series [image omitted] are universal with respect to overconvergence. Our main purpose is to solve a problem of Nestoridis. In addition some properties of univer...
作者:Wolfgang Gehlen
来源:[J].Journal of Approximation Theory(IF 0.755), 2000, Vol.106 (1), pp.110-142Elsevier
摘要:Abstract(#br)Let f ∈ C [−1, 1] be real-valued. We consider the Lipschitz constants L n ( f ) of the operators of best uniform polynomial approximation of degree n , n ∈ N . It is proved that lim sup n ∈ N L n ( f )=∞, whenever f is not a polynomial.
作者:Wolfgang Gehlen
来源:[J].Journal of Approximation Theory(IF 0.755), 1999, Vol.101 (2), pp.221-239Elsevier
摘要:Abstract(#br)Let f ∈ C [−1, 1] be real-valued. We consider the sequence of strong unicity constants ( γ n ( f )) n induced by the polynomials of best uniform approximation of f . It is proved that lim inf n →∞ γ n ( f )=0, whenever f is not a polynomial.
作者:Wolfgang Gehlen
来源:[J].Journal of Approximation Theory(IF 0.755), 1997, Vol.89 (1), pp.118-132Elsevier
摘要:Abstract(#br)We consider the sequence of errors ( E n ( f )) n of best uniform approximation to a function f ∈ C [−1, 1] by algebraic polynomials. It is shown that the regularity of f in subsets of [−1, 1] implies certain conditions on the sequence ( E n ( f )) n .
作者:Wolfgang Gehlen
来源:[J].Journal of Approximation Theory(IF 0.755), 1998, Vol.94 (3), pp.467-480Elsevier
摘要:Abstract(#br)We consider the distribution of alternation points in best real polynomial approximation of a function f ∈ C [−1, 1]. For entire functions f we look for structural properties of f that will imply asymptotic equidistribution of the corresponding alternation point...
作者:Wolfgang Gehlen
来源:[J].Journal of Mathematical Analysis and Applications(IF 1.05), 1996, Vol.198 (2), pp.490-505Elsevier
摘要:Abstract(#br)In this paper we are concerned with the size of domains of overconvergence of power series. By means of conformal maps we derive necessary conditions for a power series to admit an analytic continuation beyond a complete domain of overconvergence.

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