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Higher-order linear differential equations with solutions having a prescribed sequence of zeros and lying in the Dirichlet space

Li-Peng Xiao (2015)

Annales Polonici Mathematici

The aim of this paper is to consider the following three problems:i (1) for a given uniformly q-separated sequence satisfying certain conditions, find a coefficient function A(z) analytic in the unit disc such that f”’ + A(z)f = 0 possesses a solution having zeros precisely at the points of this sequence; (2) find necessary and sufficient conditions for the differential equation $f^{(k)} + A_{k - 1} f^{(k - 1)} + \dots + A ₁ f^{'} + A ₀ f = 0$ (*) in the unit disc to be Blaschke-oscillatory; (3) find sufficient conditions on the analytic coefficients of the...

Holomorphic foliations in $ℂ ℙ (2)$ having an invariant algebraic curve

Dominique Cerveau, Alcides Lins Neto (1991)

Annales de l'institut Fourier

We give estimations for the degree of separatrices of algebraic foliations in $CP (2)$ .

Holomorphic foliations in certain holomorphically convex domains of $ℂ^{2}$

Marco Brunella, Paulo Sad (1995)

Bulletin de la Société Mathématique de France

Holomorphic solutions to linear first-order functional differential equations.

van Brunt, Bruce, Marshall, Jonathan C. (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Hyperbolic Cauchy problem and Leray's residue formula

Susumu Tanabé (2000)

Annales Polonici Mathematici

We give an algebraic description of (wave) fronts that appear in strictly hyperbolic Cauchy problems. A concrete form of a defining function of the wave front issued from the initial algebraic variety is obtained with the aid of Gauss-Manin systems satisfied by Leray's residues.

Hypersurfaces solutions d'une equation de Pfaff analytique.

J.P. Jouanolou (1978)

Mathematische Annalen

Hypertranscendency of conjugacies in complex dynamics.

Paul-Georg Becker, Walter Bergweiler (1995)

Mathematische Annalen

Incompressibilité des feuilles de germes de feuilletages holomorphes singuliers

David Marín, Jean-François Mattei (2008)

Annales scientifiques de l'École Normale Supérieure

Nous considérons un germe de feuilletage holomorphe singulier non-dicritique $ℱ$ défini sur une boule fermée $\bar{𝔹} \subset ℂ^{2}$ , satisfaisant des hypothèses génériques, de courbe de séparatrice $S$ . Nous démontrons l’existence d’un voisinage ouvert $U$ de $S$ dans $\bar{𝔹}$ tel que, pour toute feuille $L$ de $ℱ_{| (U ∖ S)}$ , l’inclusion naturelle $ı : L ↪ U ∖ S$ induit un monomorphisme $ı_{*} : π_{1} (L) ↪ π_{1} (U ∖ S)$ au niveau du groupe fondamental. Pour cela, nous introduisons la notion géométrique de « connexité feuilletée » avec laquelle nous réinterprétons la notion d’incompressibilité....