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A Coefficient Problem for Functions Regular in an Annulus

  • M. S. Robertson (a1)

Extract

1. Introduction A solution will be given in this paper for the following problem.

Let

(1.1)

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References

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1. Dieudonné, J., Recherches sur quelques problémes relatifs aux polynomes et aux fonctions bornées d'une variable complexe, Ann. École Normale (3), vol. 48 (1931), 247358.
2. Goodman, A. W., On some determinants related to p-valent functions, Trans. Amer. Math. Soc, vol. 63 (1948), 175192.
3. Goodman, A. W. and Robertson, M. S., A class of multivalent functions, Trans. Amer. Math. Soc, vol. 70 (1951), 127136.
4. Kakeya, S., On the function whose imaginary part on the unit circle changes its sign only twice, Proc. Imp. Acad. Tokyo, vol. 18 (1942), 435439.
5. Robertson, M. S., Analytic functions star-like in one direction, Amer. J. Math., vol. 58 (1936), 465472.
6. Robertson, M. S., A representation of all analytic functions in terms of functions with positive real parts, Ann. Math., vol. 38 (1937), 770783.
7. Robertson, M. S., The variation of the sign of V for an analytic function U + iV, Duke Math. J., vol. 5 (1939), 512519.
8. Rogosinski, W., Über positive harmonische Entwicklungen und typisch-reelle Potenzreihen, Math. Z., vol. 35 (1932), 93121.
9. Szász, O., Über Funktionen, die den Einheitskreis schlicht abbilden, Jber. dtsch. MatVer. vol. 42 (1932), 7375.
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