Maximum modulus function of derivatives of entire functions defined by Dirichlet series
Maximum modulus in a bidisc of analytic functions of bounded -index and an analogue of Hayman’s theorem
We generalize some criteria of boundedness of -index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).
May the Cauchy transform of a non-trivial finite measure vanish on the support of the measure?
Mean growth and Taylor coefficients of some topological algebras of analytic functions
Meandering of trajectories of polynomial vector fields in the affine n-space.
We give an explicit upper bound for the number of isolated intersections between an integral curve of a polynomial vector field in Rn and an affine hyperplane.The problem turns out to be closely related to finding an explicit upper bound for the length of ascending chains of polynomial ideals spanned by consecutive derivatives.This exposition constitutes an extended abstract of a forthcoming paper: only the basic steps are outlined here, with all technical details being either completely omitted...
Measure density and extendability of Sobolev functions.
Measured geodesic laminations in Flatland
Since their introduction by Thurston, measured geodesic laminations on hyperbolic surfaces occur in many contexts. In this survey, we give a generalization of geodesic laminations on surfaces endowed with a half-translation structure (that is a singular flat surface with holonomy ), called flat laminations, and we define transverse measures on flat laminations similar to transverse measures on hyperbolic laminations, taking into account that the images of the leaves of a flat lamination are in...
Measures connected with Bargmann's representation of the q-commutation relation for q > 1
Classical Bargmann’s representation is given by operators acting on the space of holomorphic functions with scalar product . We consider the problem of representing the functional F as a measure. We prove the existence of such a measure for q > 1 and investigate some of its properties like uniqueness and radiality.
Meilleure approximation polynomiale et croissance des fonctions entières sur certaines variétés algébriques affines
Soit un compact polynomialement convexe de et son “potentiel logarithmique extrémal” dans . Supposons que est régulier (i.e. continue) et soit une fonction holomorphe sur un voisinage de . On construit alors une suite de polynôme de variables complexes avec deg pour , telle que l’erreur d’approximation soit contrôlée de façon assez précise en fonction du “pseudorayon de convergence” de par rapport à et du degré de convergence . Ce résultat est ensuite utilisé pour étendre...
Meilleures estimations possibles pour l'ensemble des points algébriques de fonctions analytiques.
Mémoire sur les fonctions analytiques uniformes. Traduit par E. Picard
Mercerian Theorems Involving Cesàro Means of Positive Order.
Meromorphe Approximationen
Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen.
Meromorphic extendibility and the argument principle.
Meromorphic function sharing a small function with a linear differential polynomial
The problem of uniqueness of an entire or a meromorphic function when it shares a value or a small function with its derivative became popular among the researchers after the work of Rubel and Yang (1977). Several authors extended the problem to higher order derivatives. Since a linear differential polynomial is a natural extension of a derivative, in the paper we study the uniqueness of a meromorphic function that shares one small function CM with a linear differential polynomial, and prove the...
Meromorphic Function Sharinga Small Function with its Differential Polynomial
In this paper we improve, generalize and extend a number of recent results related to a problem of meromorphic function sharing a small function with its differential polynomial which are the continuation of a result earlier obtained by R. Brück.
Meromorphic function that shares one small function with its derivative.
Meromorphic functions and also their first two derivatives have the same zeros.
Meromorphic functions of infinite order in the angular domain
We investigate the value distribution of meromorphic functions in the angular domain. In particular, we show a close relationship between radially distributed values and Borel directions of transcendental meromorphic functions of infinite order in some angular domains.