Kompakte Summierbarkeit von Potenzreihen im Einheitskreis

Ohne Zusammenfassung     

Über cluster sets analytischer Funktionen

Ohne ZusammenfassungHerrn Professor Georg Alexits zum 80. Geburtstag gewidmet     

Polynomial series expansions for confluent and Gaussian hypergeometric functions

Based on the Hadamard product of power series, polynomial series expansions for confluent hypergeometric functions and for Gaussian hypergeometric functions are introduced and studied. It turns out that the partial sums provide an interesting alternative for the numerical evaluation of the functions and , in particular, if the parameters are also viewed as variables.

     

Transition from disorder to order in thin metallic films studied with angle-resolved photoelectron spectroscopy

The transition from disorder to order in Ag film grown on Au(111) was investigated by monitoring the quantum well states using angle-resolved photoelectron spectroscopy. Our results show that the binding energies do not alter, but the in-plane dispersion alters from flat to parabolic when the film is annealed. We suggest that there are isolated and ordered patches scattered across the film at an early stage of the transition and that atoms inside the patches are fully ordered along the surface normal. These ordered patches grow and merge together as the annealing temperature increases.     

Universal meromorphic approximation on Vitushkin sets

The paper proves the following result on universal meromorphic approximation: Given any unbounded sequence {λ _n } ? ?, there exists a function ?, meromorphic on ?, with the following property. For every compact set K of rational approximation (i.e. Vitushkin set), and every function f, continuous on K and holomorphic in the interior of K, there exists a subsequence {n _k } of ? such that $ \left\{ {\varphi \left( {z + \lambda _{n_k } } \right)} \right\} The paper proves the following result on universal meromorphic approximation: Given any unbounded sequence {λ _n } ⊂ ℂ, there exists a function ϕ, meromorphic on ℂ, with the following property. For every compact set K of rational approximation (i.e. Vitushkin set), and every function f, continuous on K and holomorphic in the interior of K, there exists a subsequence {n _k } of ℕ such that converges to f(z) uniformly on K. A similar result is obtained for arbitrary domains G ≠ ℂ. Moreover, in case {λ _n }={n} the function ϕ is frequently universal in terms of Bayart/Grivaux [3]. Original Russian Text ? W.Luh, T.Meyrath, M.Niess, 2008, published in Izvestiya NAN Armenii. Matematika, 2008, No. 6, pp. 66–75.