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A variational method for univalent functions connected with antigraphy

Janina Macura (1996)

Banach Center Publications

The paper is devoted to a class of functions analytic and univalent in the unit disk that are connected with an antigraphy e i φ ω ¯ + i ρ e i φ / 2 . Variational formulas and Grunsky inequalities are derived. As an application there are given some estimations in the considered class of functions.

About the generating function of a left bounded integer-valued random variable

Charles Delorme, Jean-Marc Rinkel (2008)

Bulletin de la Société Mathématique de France

We give a relation between the sign of the mean of an integer-valued, left bounded, random variable X and the number of zeros of 1 - Φ ( z ) inside the unit disk, where Φ is the generating function of X , under some mild conditions

Admissible functions for the Dirichlet space

Javad Mashreghi, Mahmood Shabankhah (2010)

Studia Mathematica

Zero sets and uniqueness sets of the classical Dirichlet space are not completely characterized yet. We define the concept of admissible functions for the Dirichlet space and then apply them to obtain a new class of zero sets for . Then we discuss the relation between the zero sets of and those of .

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