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Radial Averaging Transformations and Generalized Capacities.

Catherine Bandle, Moshe Marcus (1975)

Mathematische Zeitschrift

Radial growth and variation of univalent functions and of Dirichlet finite holomorphic functions

Daniel Girela (1996)

Colloquium Mathematicae

A well known result of Beurling asserts that if f is a function which is analytic in the unit disc $Δ = z \in ℂ : | z | < 1$ and if either f is univalent or f has a finite Dirichlet integral then the set of points $e^{i θ}$ for which the radial variation $V (f, e^{i θ}) = \int_{0}^{1} | f^{'} (r e^{i θ}) | d r$ is infinite is a set of logarithmic capacity zero. In this paper we prove that this result is sharp in a very strong sense. Also, we prove that if f is as above then the set of points $e^{i θ}$ such that $(1 - r) | f^{'} (r e^{i θ}) | \neq o (1)$ as r → 1 is a set of logarithmic capacity zero. In particular, our results give...

Radial growth of the derivative of univalent functions.

T.H. MacGregor, J.G. Clunie (1984)

Commentarii mathematici Helvetici

Radial segments and conformal mapping of an annulus onto domains bounded by a circle and a k-circle

Tetsuo Inoue (1992)

Annales Polonici Mathematici

Let f(z) be a conformal mapping of an annulus A(R) = 1 < |z| < R and let f(A(R)) be a ring domain bounded by a circle and a k-circle. If R(φ) = w : arg w = φ, and l(φ) - 1 is the linear measure of f(A(R)) ∩ R(φ), then we determine the sharp lower bound of $l (φ_{1}) + l (φ_{2})$ for fixed $φ_{1}$ and $φ_{2}$ $(0 \leq ...$

Radii of p-valence of certain analytic functions of order $α$ with negative coefficients

M. K. Aouf (1989)

Matematički Vesnik

Radii of starlikeness and coefficient estimates of a class of analytic functions

Om Prakash Ahuja (1983)

Časopis pro pěstování matematiky

Radius estimates of a subclass of univalent functions

Maslina Darus, Rabha W. Ibrahim (2011)

Matematički Vesnik

Radius of strongly starlikeness for certain analytic functions.

Kwon, Oh Sang, Owa, Shigeyoshi (2002)

International Journal of Mathematics and Mathematical Sciences

Radius problems for a subclass of close-to-convex univalent functions.

Noor, Khalida Inayat (1992)

International Journal of Mathematics and Mathematical Sciences

Random polynomials and (pluri)potential theory

Thomas Bloom (2007)

Annales Polonici Mathematici

For certain ensembles of random polynomials we give the expected value of the zero distribution (in one variable) and the expected value of the distribution of common zeros of m polynomials (in m variables).

Randschlichte meromorphe Funktionen auf endlichen Riemannschen Flächen.

Steffen Timmann, Helmut Köditz (1975)

Mathematische Annalen

Rate of growth of polynomials not vanishing inside a circle.

Gardner, Robert B., Govil, N.K., Musukula, Srinath R. (2005)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Ray sequences of Laurent-type rational functions.

Pritsker, I.E. (1996)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Real and complex pseudozero sets for polynomials with applications

Stef Graillat, Philippe Langlois (2007)

RAIRO - Theoretical Informatics and Applications

Pseudozeros are useful to describe how perturbations of polynomial coefficients affect its zeros. We compare two types of pseudozero sets: the complex and the real pseudozero sets. These sets differ with respect to the type of perturbations. The first set – complex perturbations of a complex polynomial – has been intensively studied while the second one – real perturbations of a real polynomial – seems to have received little attention. We present a computable formula for the real pseudozero...

Real $C^{k}$ Koebe principle

Weixiao Shen, Michael Todd (2005)

Fundamenta Mathematicae

We prove a $C^{k}$ version of the real Koebe principle for interval (or circle) maps with non-flat critical points.

Currently displaying 1 – 20 of 53