A bounded analytic function in the unit disk with a level set component of infinite length
Authors:
K. F. Barth and J. G. Clunie
Journal:
Proc. Amer. Math. Soc. 85 (1982), 562566
MSC:
Primary 30D50
MathSciNet review:
660605
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Abstract: The authors construct a bounded analytic function in the unit disk with a level set component of infinite length. The example is of the form where is a Blaschke Product.
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 J. B. Garnett, F. W. Gehring and P. W. Jones, Level sets for univalent functions and a theorem of Fejér and Riesz (to appear).
 [3]
 W. K. Hayman and J.M. G. Wu, Level sets of univalent functions, Comment. Math. Helv. 56 (1981), 366403. MR 639358 (83b:30008)
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 P. W. Jones, Bounded holomorphic functions with all level sets of infinite length, Michigan Math. J. 27 (1980), 7580. MR 555839 (81b:30066)
 [5]
 G. Piranian, Inner functions with a levelset of infinite length, Complex Analysis, Joensuu, 1978 (Proc. Colloq., Univ. Joensuu, Joensuu, 1978), Lecture Notes in Math., vol. 747, SpringerVerlag, Berlin and New York, 1979, pp. 309313. MR 553057 (80j:30045)
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 G. Piranian and A. Weitsman, Level sets of infinite length, Comment. Math. Helv. 53 (1978), 161164. MR 490872 (81j:30029)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198206606059
PII:
S 00029939(1982)06606059
Keywords:
Bounded functions,
level set,
level curve
Article copyright:
© Copyright 1982
American Mathematical Society
