Über die Konvergenz der Orthogonalpolynomreihe einer Funktion mit beschränkter Variation
Ueber eine Eigenschaft der Coefficienten in der Taylor'schen Reihe
Under which conditions is the Jacobi space subset of ?
Exact conditions for α, β, a, b > −1 and 1 ≤ p ≤ ∞ are determined under which the inclusion property ⊂ is valid. It is shown that the conditions characterize the inclusion property. The paper concludes with some results, in which the inclusion property can be detected in relation with estimates of Jacobi differential operators and with Muckenhoupt’s transplantation theorems and multiplier theorems for Jacobi series.
Une formule d'interpolation en deux variables
On démontre une formule d’interpolation pour une fonction de deux variables complexes qui tient compte des valeurs de cette fonction ainsi que de ses dérivées partielles par rapport à en des points d’un sous-groupe de de rang . On explique préalablement comment, dans les grandes lignes, une telle formule permet de ramener la conjecture de Schanuel à un énoncé dont la forme est celle d’un critère d’indépendance algébrique.
Uniform approximation by incomplete polynomials.
Uniform approximation by polynomials on real non-degenerate Weil polyhedron.
Uniform Approximation by Spherical Spline Interpolation.
Uniform approximation with linear combinations of reproducing kernels
We show several theorems on uniform approximation of functions. Each of them is based on the choice of a special reproducing kernel in an appropriate Hilbert space. The theorems have a common generalization whose proof is founded on the idea of the Kaczmarz projection algorithm.
Uniform convergence of Lienhard's spline approximations of a given continuous function.
Universally optimal approximation of functionals
A universal optimal in order approximation of a general functional in the space of continuous periodic functions is constructed and its fundamental properties and some generalizations are investigated. As an application the approximation of singular integrals is considered and illustrated by numerical results.
Untersuchungen über das Wachstum von Potenzreihenabschnitten mit Anwendungen für das Hornerschema.