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Displaying 21 – 40 of 51

On the complexification of real-analytic polynomial mappings of ℝ²

Ewa Ligocka (2006)

Annales Polonici Mathematici

We give a simple algebraic condition on the leading homogeneous term of a polynomial mapping from ℝ² into ℝ² which is equivalent to the fact that the complexification of this mapping can be extended to a polynomial endomorphism of ℂℙ². We also prove that this extension acts on ℂℙ²∖ℂ² as a quotient of finite Blaschke products.

On the extendability of quadratic polynomial mappings of the plane

Ewa Ligocka (2009)

Annales Polonici Mathematici

We shall prove, using the result from our previous paper [Ann. Polon. Math. 88 (2006)], that for a quadratic polynomial mapping Q of ℝ² only the geometric shape of the critical set of Q determines whether the complexification of Q can be extended to an endomorphism of ℂℙ². At the end of the paper we describe some interesting classes of quadratic polynomial mappings of ℝ² and give some examples.

On the Extreme Points of a Subclass of Holomorphic Functions with Positive Real Part.

N. Samaris (1986)

Mathematische Annalen

On the Hausdorff dimension of a Julia set with a rationally indifferent periodic point

M. Urbański (1990)

Studia Mathematica

On the Zeros of Functions in the Bers Space

A. Fletcher, V. Marković (2004)

Publications de l'Institut Mathématique

Perturbative computation of analytic invariants of resonant diffeomorphisms of $(C, 0)$

Ezio Todesco, Julio Cesar Canille Martins (1996)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Pick-Nevanlinna interpolation on finitely-connected domains

Stephen Fisher (1992)

Studia Mathematica

Let Ω be a domain in the complex plane bounded by m+1 disjoint, analytic simple closed curves and let $z_{0}, . . ., z_{n}$ be n+1 distinct points in Ω. We show that for each (n+1)-tuple $(w_{0}, . . ., w_{n})$ of complex numbers, there is a unique analytic function B such that: (a) B is continuous on the closure of Ω and has constant modulus on each component of the boundary of Ω; (b) B has n or fewer zeros in Ω; and (c) $B (z_{j}) = w_{j}$ , 0 ≤ j ≤ n.