Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On bounded oscillation and asymptotic expansion of conformal strip mappings


Author: Arthur E. Obrock
Journal: Trans. Amer. Math. Soc. 173 (1972), 183-201
MSC: Primary 30A30
MathSciNet review: 0310214
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Relations between the boundary parameters $ {\phi _ - },{\phi _ + }$ of a strip $ S = \{ {\phi _ - }(x) < y < {\phi _ + }(x)\} $ and the values $ f(x)$ of its canonical conformal mapping onto a horizontal strip $ H = \{ \vert\upsilon \vert < 1\} $ are studied. Bounded oscillation $ ({\max _y}\operatorname{Re} f(x + iy) - {\min _y}\operatorname{Re} f(x + iy) = \omega (x) = O(1))$ is characterized in terms of $ {\phi _ - },{\phi _ + }$. A formal series expansion $ \upsilon = \sum {y^m}{a_{m,n}}(x)$ is derived for the solution to the Dirichlet problem on $ S$ and its partial sums are used to obtain formulas for the asymptotic expansion of $ f$ in terms of $ {\phi _ + },{\phi _ - }$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30A30

Retrieve articles in all journals with MSC: 30A30


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0310214-4
PII: S 0002-9947(1972)0310214-4
Keywords: Conformal strip mappings, Ahlfors Distortion Theorem, Warschawski formula, the formula of Gol'dberg and Stročik, extremal length, Dirichlet problem, quasiconformal mapping, the Theorem of Teichmüller, Wittich and Belinski
Article copyright: © Copyright 1972 American Mathematical Society