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1
Content available remote

On locally biholomorphic surjective mappings

100%
Ligocka E.
Annales Polonici Mathematici
|
2003
|
tom 82
|
nr 2
127-135
EN
We prove that each open Riemann surface can be locally biholomorphically (locally univalently) mapped onto the whole complex plane. We also study finite-to-one locally biholomorphic mappings onto the unit disc. Finally, we investigate surjective biholomorphic mappings from Cartesian products of domains.
2
Content available remote

On extensions of the Mittag-Leffler theorem

100%
Ligocka E.
Annales Polonici Mathematici
|
1998
|
tom 68
|
nr 3
249-256
EN
The classical Mittag-Leffler theorem on meromorphic functions is extended to the case of functions and hyperfunctions belonging to the kernels of linear partial differential operators with constant coefficients.
3
Content available remote

On the uniformization of Hartogs domains in $ℂ^2$ and their envelopes of holomorphy

100%
Ligocka E.
Colloquium Mathematicum
|
1998
|
tom 77
|
nr 2
265-269
4
Content available remote

On Some Correspondence between Holomorphic Functions in the Unit Disc and Holomorphic Functions in the Left Halfplane

100%
Ligocka E.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2009
|
tom 57
|
nr 3
223-229
EN
We study a correspondence L between some classes of functions holomorphic in the unit disc and functions holomorphic in the left halfplane. This correspondence is such that for every f and w ∈ ℍ, exp(L(f)(w)) = f(expw). In particular, we prove that the famous class S of univalent functions on the unit disc is homeomorphic via L to the class S(ℍ) of all univalent functions g on ℍ for which g(w+2πi) = g(w) + 2πi and $lim_{Re z→-∞}(g(w)-w) = 0$.
5
Content available remote

On complexification and iteration of quasiregular polynomials which have algebraic degree two

100%
Ligocka E.
Fundamenta Mathematicae
|
2005
|
tom 186
|
nr 3
269-285
EN
We prove that each degree two quasiregular polynomial is conjugate to Q(z) = z² - (p+q)|z|² + pqz̅² + c, |p| < 1, |q| < 1. We also show that the complexification of Q can be extended to a polynomial endomorphism of ℂℙ² which acts as a Blaschke product (z-p)/(1-p̅z) · (z-q)/(1-q̅z) on ℂℙ²∖ℂ². Using this fact we study the dynamics of Q under iteration.
6
Content available remote

Elementary proofs of the Liouville and Bôcher theorems for polyharmonic functions

100%
Ligocka E.
Annales Polonici Mathematici
|
1998
|
tom 68
|
nr 3
257-265
EN
Elementary proofs of the Liouville and Bôcher theorems for polyharmonic functions are given. These proofs are on the calculus level and use only the basic knowledge of harmonic functions given in Axler, Bourdon and Ramey's book.
7
Content available remote

Remarks on the Bergman kernel function of a worm domain

100%
Ligocka E.
Studia Mathematica
|
1998
|
tom 130
|
nr 2
109-113
EN
We use a recent result of M. Christ to show that the Bergman kernel function of a worm domain cannot be $C^∞$-smoothly extended to the boundary.
8
Content available remote

On the extendability of quadratic polynomial mappings of the plane

100%
Ligocka E.
Annales Polonici Mathematici
|
2009
|
tom 96
|
nr 3
283-294
EN
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.
9
Content available remote

On the Hartogs-type series for harmonic functions on Hartogs domains in $ℝ^n × ℝ^m$, m ≥ 2

100%
Ligocka E.
Annales Polonici Mathematici
|
1999
|
tom 71
|
nr 2
151-160
EN
We study series expansions for harmonic functions analogous to Hartogs series for holomorphic functions. We apply them to study conjugate harmonic functions and the space of square integrable harmonic functions.
10
Content available remote

Corrigendum to the paper "On the reproducing kernel for harmonic functions and the space of Bloch harmonic functions on the unit ball in R^{n}" (Studia Mathematica 87 (1987), 23-32)

100%
Ligocka E.
Studia Mathematica
|
1991-1992
|
tom 101
|
nr 3
319
11
Content available remote

On fixed points of holomorphic type

100%
Ligocka E.
Colloquium Mathematicum
|
2002
|
tom 94
|
nr 1
61-66
EN
We study a linearization of a real-analytic plane map in the neighborhood of its fixed point of holomorphic type. We prove a generalization of the classical Koenig theorem. To do that, we use the well known results concerning the local dynamics of holomorphic mappings in ℂ².
12
Content available remote

On the complexification of real-analytic polynomial mappings of ℝ²

100%
Ligocka E.
Annales Polonici Mathematici
|
2006
|
tom 88
|
nr 2
119-125
EN
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.
13
Content available remote

On the dynamics of extendable polynomial endomorphisms of ℝ²

100%
Ligocka E.
Annales Polonici Mathematici
|
2007
|
tom 90
|
nr 1
37-50
EN
We extend the results obtained in our previous paper, concerning quasiregular polynomials of algebraic degree two, to the case of polynomial endomorphisms of ℝ² whose algebraic degree is equal to their topological degree. We also deal with some other classes of polynomial endomorphisms extendable to ℂℙ².
14
Content available remote

On the injectivity of the generalized Bers projection and its Fréchet derivative

100%
Ligocka E.
Colloquium Mathematicum
|
1994
|
tom 67
|
nr 2
181-186
15
Content available remote

On quasiregular polynomial mappings

100%
Ligocka E.
Colloquium Mathematicum
|
1998
|
tom 75
|
nr 1
79-89
16
Content available remote

On Dittmar's approach to the Beltrami equation

100%
Ligocka E.
Colloquium Mathematicum
|
2002
|
tom 92
|
nr 2
189-195
EN
We recall an old result of B. Dittmar. This result permits us to obtain an existence theorem for the Beltrami equation and some other results as a direct consequence of Moser's classical estimates for elliptic operators.
17
Content available remote

Estimates in Sobolev norms $∥ ·∥^{s}_{p}$ for harmonic and holomorphic functions and interpolation between Sobolev and Hölder spaces of harmonic functions

75%
Ligocka E.
Studia Mathematica
|
1987
|
tom 86
|
nr 3
255-271
18
Content available remote

On the reproducing kernel for harmonic functions and the space of Bloch harmonic functions on the unit ball in $R^{n}$

63%
Ligocka E.
Studia Mathematica
|
1987
|
tom 87
|
nr 1
23-32
19
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Levi forms, differential forms of type (0,1) and pseudoconvexity in Banach spaces

51%
Ligocka E.
Annales Polonici Mathematici
|
1976-1977
|
tom 33
|
nr 1
63-69
20
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

How to prove Fefferman's theorem without use of differential geometry

51%
Ligocka E.
Annales Polonici Mathematici
|
1981
|
tom 39
|
nr 1
117-130
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