Acta Mathematica

A converse of Cauchy's theorem and applications to extremal problems

Arthur H. Read

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Acta Math., Volume 100, Number 1-2 (1958), 1-22.

First available in Project Euclid: 31 January 2017

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1958 © Almqvist & Wiksells Boktryckeri


Read, Arthur H. A converse of Cauchy's theorem and applications to extremal problems. Acta Math. 100 (1958), no. 1-2, 1--22. doi:10.1007/BF02559600.

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  • L. V. Ahlfors, Open Riemann surfaces and extremal problem on compact subregions. Comment. Math. Helv. 24 (1950).
  • L. V. Ahlfors, Variational methods in function theory. (Lectures at Harvard University, 1953, transcribed by E. C. Schlesinger.)
  • S. Banach, Théorie des opérations linéaires. Warsaw, 1932.
  • C. Caratheodory, Theory of Functions of a Complex Variable. New York, 1954.
  • P. Garabedian, Schwarz's Lemma and the Szegö kernel function. Trans. Amer. Math. Soc., 67 (1949).
  • P. Garabedian, The classes Lp and conformal mapping. Trans. Amer. Math. Soc., 69 (1950).
  • P. D. Lax, Reciprocal extremal problems in function theory. Comm. Pure Appl. Math., 8 (1955).
  • R. Nevanlinna, Uniformisierung. Berlin, 1953.
  • W. F. Osgood, Lehrbuch der Funktiontheorie, Band II, 2. Leipzig, 1932.
  • A. H. Read, Harvard Thesis (not in print).
  • A. H. Read, Conjugate exfremal problem of class p=1. Ann. Ac. Sci. Fenn. To appear.
  • W. Rudin, Analytic functions of class Hp. Trans. Amer. Math. Soc., 78 (1955).
  • W. W. Rogosinski & H. S. Shapiro, On certain extrenum problems for analytic functions. Acta Math., 90, (1950).
  • V. Smirnoff, Sur les valeurs limites des fonctions analytiques. C. R., 188 (1929), pp. 131–133.
  • A. Zygmund, Trigonometrical Series, New York, 1952.
  • J. L. Doob, A minimum problem in the theory of analytic functions. Duke Math. J., 8 (1941).