The Löwner-Kufarev representations for domains with analytic boundaries
Annales UMCS, Mathematica (2011)
- Volume: 65, Issue: 2, page 139-148
- ISSN: 2083-7402
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topDmitri Prokhorov. "The Löwner-Kufarev representations for domains with analytic boundaries." Annales UMCS, Mathematica 65.2 (2011): 139-148. <http://eudml.org/doc/268335>.
@article{DmitriProkhorov2011,
abstract = {We consider the Löwner-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 Löwner-Kufarev chain consisting of univalent quadratic polynomials and compare the Löwner-Kufarev representations of bounded and arbitrary univalent functions.},
author = {Dmitri Prokhorov},
journal = {Annales UMCS, Mathematica},
keywords = {Löwner-Kufarev equation; analytic continuation; univalent polynomials; bounded univalent functions; univalent function; Loewner chain; subordination chain; parametric method; holomorphic extension; analytic extension; bounded univalent function},
language = {eng},
number = {2},
pages = {139-148},
title = {The Löwner-Kufarev representations for domains with analytic boundaries},
url = {http://eudml.org/doc/268335},
volume = {65},
year = {2011},
}
TY - JOUR
AU - Dmitri Prokhorov
TI - The Löwner-Kufarev representations for domains with analytic boundaries
JO - Annales UMCS, Mathematica
PY - 2011
VL - 65
IS - 2
SP - 139
EP - 148
AB - We consider the Löwner-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 Löwner-Kufarev chain consisting of univalent quadratic polynomials and compare the Löwner-Kufarev representations of bounded and arbitrary univalent functions.
LA - eng
KW - Löwner-Kufarev equation; analytic continuation; univalent polynomials; bounded univalent functions; univalent function; Loewner chain; subordination chain; parametric method; holomorphic extension; analytic extension; bounded univalent function
UR - http://eudml.org/doc/268335
ER -
References
top- Kufarev, P. P., On one-parametric families of analytic functions, Mat. Sbornik N. S. 13(55) (1943), 87-118 (Russian).
- Löwner, K., Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I, Math. Ann. 89 (1923), no. 1-2, 103-121. Zbl49.0714.01
- Markina, I., Vasil'ev, A., Virasoro algebra and dynamics in the space of univalent functions, Contemp. Math. 525 (2010), 85-116. Zbl1234.81127
- Pommerenke, Ch., Über die Subordination analytischer Funktionen, J. Reine Angew. Math. 218 (1965), 159-173. Zbl0184.30601
- Pommerenke, Ch., Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, 1975.
- Roth, O., Schippers, E., The Loewner and Hadamard variations, Illinois J. Math. 52 (2008), no. 4, 1399-1415. Zbl1187.30005
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