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On extreme Bloch functions with prescribed critical points. (English) Zbl 0482.30023


MSC:

30D45 Normal functions of one complex variable, normal families
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30F10 Compact Riemann surfaces and uniformization

Citations:

Zbl 0377.30035
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References:

[1] Aharonov, D., Shapiro, H.S.: Domains on which analytic functions satisfy quadrature identities. J. Analyse Math.30, 39-73 (1976) · Zbl 0337.30029 · doi:10.1007/BF02786704
[2] Cima, J.A., Wogen, W.R.: Extreme points of the unit ball of the Bloch spaceB 0. Michigan Math. J.25, 213-222 (1978) · Zbl 0377.30035 · doi:10.1307/mmj/1029002062
[3] Davis, P.J.: The Schwarz functions and its applications. Washington: Mathematical Association of America 1974 · Zbl 0293.30001
[4] Peschl, E.: Les invariants différentiels non holomorphes et leur rôle dans la théorie des fonctions. Rend. Sem. Mat. Messina1, 100-108 (1955)
[5] Peschl, E.: Über die Weiterentwicklung einer Majorisierungsmethode der Funktionentheorie, die auf Differentialinvarianten aufbaut. In: C. Carathéodory, International Symposium (Athens 1973), pp. 461-482. Athens: The Greek Mathematical Society 1974
[6] Ruscheweyh, St.: Gewisse Klassen verallgemeinerter analytischer Funktionen. Bonner Mathematische Schriften39. Bonn: Mathematisches Institut der Universität 1969 · Zbl 0223.35026
[7] Wirths, K.-J.: Über holomorphe Funktionen, die einer Wachstumsbeschränkung unterliegen. Arch. Math. (Basel)30, 606-612 (1978) · Zbl 0373.30016
[8] Wirths, K.-J.: On holomorphic functions satisfying |f(z)|(1?|z|2 ? 1 in the unit disc. Preprint · Zbl 0484.30001
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