Ueber eine besondere Gattung von singulären Stellen analytischer Functionen
Ueber eine Verallgemeinung der Taylorschen Reihe
Ueber Reihenentwicklung nach Bessel'schen Functionen
Ueber Vereinfachungen in der elementaren Theorie der analytischen Funktionen
Ultraconvergence et singularités pour une classe de séries d'exponentielles
Localisation des singularités des fonctions analytiques définies par des séries du type exp, où les sont complexes et où les sont des polynômes tayloriens, en utilisant des propriétés obtenues selon deux méthodes originellement dues l’une à B. Lepson pour les séries d’exponentielles à coefficients polynomiaux et dont la suite des exposants est une -suite et l’autre à G. L. Luntz pour les séries de Taylor-Dirichlet. Le résultat fondamental utilise un théorème de A. F. Leont’ev-G. P. Lapin...
Un Théorème sur les Séries de Dirichlet.
Une généralisation du développement en fraction continue
Uniform approximation by polynomials in two functions.
Uniform convergence of power series expansions on the boundary.
Uniqueness theorems
Uniqueness Theorems for Bounded Holomorphic Functions.
Univalence of odd derivatives of even entire functions.
Universal approximation theorem for Dirichlet series.
Universal functions on nonsimply connected domains
We establish certain properties for the class of universal functions in with respect to the center , for certain types of connected non-simply connected domains . In the case where is discrete we prove that this class is -dense in , depends on the center and that the analog of Kahane’s conjecture does not hold.
Universal Taylor series
We strengthen a result of Chui and Parnes and we prove that the set of universal Taylor series is a -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.
Universal Taylor series, conformal mappings and boundary behaviour
A holomorphic function on a simply connected domain is said to possess a universal Taylor series about a point in if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta outside (provided only that has connected complement). This paper shows that this property is not conformally invariant, and, in the case where is the unit disc, that such functions have extreme angular boundary behaviour.
Universal Taylor series with maximal cluster sets.
Universally divergent Fourier series via Landau's extremal functions
We prove the existence of functions , the Fourier series of which being universally divergent on countable subsets of . The proof is based on a uniform estimate of the Taylor polynomials of Landau’s extremal functions on .