Pairs of paths and critical points.
The authors construct a periodic quasiregular function of any finite order p, 1 < p < infinity. This completes earlier work of O. Martio and U. Srebro.
L'objet de ce texte est de donner une estimation arithmétique des valeurs prises par les polynômes de Lagrange sur les entiers d'un corps quadratique imaginaire en des points de ce corps. Ces polynômes interviennent dans l'étude des fonctions entières arithmétiques et dans les minorations de formes linéaires de Logarithmes.
We prove that the Julia set of a rational map of the Riemann sphere satisfying the Collet-Eckmann condition and having no parabolic periodic point is mean porous, if it is not the whole sphere. It follows that the Minkowski dimension of the Julia set is less than 2.
Firstly, we give extensions of results of Gelfand, Esterle and Katznelson--Tzafriri on power-bounded operators. Secondly, some results and questions relating to power-bounded elements in the unitization of a commutative radical Banach algebra are discussed.
The purpose of this paper is (1) to highlight some recent and heretofore unpublished results in the theory of multiplier sequences and (2) to survey some open problems in this area of research. For the sake of clarity of exposition, we have grouped the problems in three subsections, although several of the problems are interrelated. For the reader’s convenience, we have included the pertinent definitions, cited references and related results, and in several instances, elucidated the problems by...