Sets of Uniqueness for Univalent Functions
Canadian mathematical bulletin, Tome 43 (2000) no. 1, pp. 105-107

Voir la notice de l'article provenant de la source Cambridge University Press

We observe that any set of uniqueness for the Dirichlet space $\mathcal{D}$ is a set of uniqueness for the class $S$ of normalized univalent holomorphic functions.
DOI : 10.4153/CMB-2000-016-x
Mots-clés : 30C55, 30C15
Overholt, Marius. Sets of Uniqueness for Univalent Functions. Canadian mathematical bulletin, Tome 43 (2000) no. 1, pp. 105-107. doi: 10.4153/CMB-2000-016-x
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[1] [1] Bogdan, K., On the zeros of functions with finite Dirichlet integral. Kodai Math. J. 19 (1996), 7–16. Google Scholar

[2] [2] Caughran, J. G., Two results concerning the zeros of functions with finite Dirichlet integral. Canad. J. Math. 21 (1969), 312–316. Google Scholar

[3] [3] Duren, P. L., Univalent Functions. Springer-Verlag, New York, 1983. Google Scholar

[4] [4] Duren, P. L., Problem 6.83. In: Research Problems in Complex Analysis (Eds. K. F. Barth, D. A. Brannan and W. K. Hayman), Bull. Lond.Math. Soc. 16 (1984), 490–517. Google Scholar

[5] [5] Lappan, P., Points Where Univalent Functions May Coincide. Complex Variables 5 (1985), 17–20. Google Scholar

[6] [6] Nagel, A., Rudin, W. and Shapiro, J. H., Tangential boundary behavior of functions in Dirichlet-type spaces. Ann. of Math. 116 (1982), 331–360. Google Scholar

[7] [7] Obrock, A., Problem 2.2. In: Problems in Complex Function Theory (Ed. Ch. Pommerenke), Bull. Lond. Math. Soc. 4 (1972), 354–366. Google Scholar

[8] [8] Shapiro, H. S. and Shields, A. L., On the zeros of functions with finite Dirichlet integral and some related function spaces. Math. Z. 80 (1962), 217–229. Google Scholar

[9] [9] Stegbuchner, H., Carleson sets and fixed-points of schlicht functions. Romanian-Finnish Seminar in Complex Analysis (Proc., Bucharest, 1976), 373–388, Lecture Notes in Math. 743, Springer-Verlag, Berlin, 1979. Google Scholar

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