The Lowner-Kufarev representations for domains with analytic boundaries
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2011)
- Volume: 65, Issue: 2
- ISSN: 0365-1029
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topDmitri Prokhorov. "The Lowner-Kufarev representations for domains with analytic boundaries." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 65.2 (2011): null. <http://eudml.org/doc/289818>.
@article{DmitriProkhorov2011,
abstract = {We consider the Lowner-Kufarev differential equations generating univalent maps of the unit disk onto domains bounded by analytic Jordan curves. A solution to the problem of the maximal lifetime shows how long a representation of such functions admits using infinitesimal generators analytically extendable outside the unit disk. We construct a Lowner-Kufarev chain consisting of univalent quadratic polynomials and compare the Lowner-Kufarev representations of bounded and arbitrary univalent functions.},
author = {Dmitri Prokhorov},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Lowner-Kufarev equation; analytic continuation; univalent polynomials; bounded univalent functions},
language = {eng},
number = {2},
pages = {null},
title = {The Lowner-Kufarev representations for domains with analytic boundaries},
url = {http://eudml.org/doc/289818},
volume = {65},
year = {2011},
}
TY - JOUR
AU - Dmitri Prokhorov
TI - The Lowner-Kufarev representations for domains with analytic boundaries
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2011
VL - 65
IS - 2
SP - null
AB - We consider the Lowner-Kufarev differential equations generating univalent maps of the unit disk onto domains bounded by analytic Jordan curves. A solution to the problem of the maximal lifetime shows how long a representation of such functions admits using infinitesimal generators analytically extendable outside the unit disk. We construct a Lowner-Kufarev chain consisting of univalent quadratic polynomials and compare the Lowner-Kufarev representations of bounded and arbitrary univalent functions.
LA - eng
KW - Lowner-Kufarev equation; analytic continuation; univalent polynomials; bounded univalent functions
UR - http://eudml.org/doc/289818
ER -
References
top- Kufarev, P. P., On one-parametric families of analytic functions, Mat. Sbornik N. S. 13(55) (1943), 87-118 (Russian).
- Lowner, K., Untersuchungen uber schlichte konforme Abbildungen des Einheitskreises. I, Math. Ann. 89 (1923), no. 1-2, 103-121.
- Markina, I., Vasil’ev, A., Virasoro algebra and dynamics in the space of univalent functions, Contemp. Math. 525 (2010), 85-116.
- Pommerenke, Ch., Uber die Subordination analytischer Funktionen, J. Reine Angew. Math. 218 (1965), 159-173.
- Pommerenke, Ch., Univalent Functions, Vandenhoeck & Ruprecht, Gottingen, 1975.
- Roth, O., Schippers, E., The Loewner and Hadamard variations, Illinois J. Math. 52 (2008), no. 4, 1399-1415.
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