Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the real parts of the zeros of complex polynomials and applications to continued fraction expansions of analytic functions


Author: Evelyn Frank
Journal: Trans. Amer. Math. Soc. 62 (1947), 272-283
MSC: Primary 41.1X
DOI: https://doi.org/10.1090/S0002-9947-1947-0021626-6
MathSciNet review: 0021626
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] H. Bilharz, Bemerkung zu einem Satze von Hurwitz, Zeitschrift für angewandte Mathematik und Mechanik vol. 24 (1944) pp. 77-82 (lithoprinted by Edwards Brothers, Ann Arbor, Mich., 1945). MR 0012710 (7:62h)
  • [2] C. Carathéodory, Über den Variabilitatsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen, Math. Ann. vol. 64 (1907) pp. 95-115. MR 1511425
  • [3] E. Frank, On the zeros of polynomials with complex coefficients, Bull. Amer. Math. Soc. vol. 52 (1946) pp. 144-157. MR 0014509 (7:295d)
  • [4] -, The location of the zeros of polynomials with complex coefficients, Bull. Amer. Math. Soc. vol. 52 (1946) pp. 890-898. MR 0017440 (8:154a)
  • [5] J. Geronimus, On polynomials orthogonal on the circle, on trigonometric moment-problem and on allied Carathéodory and Schur functions, preliminary announcement, C. R. (Doklady) Acad. Sci. URSS. vol. 39 (1943) pp. 291-295; Rec. Math. (Mat. Sbornik) N.S. vol. 15 (1944) pp. 99-130. MR 0012715 (7:63e)
  • [6] I. Schur, Über Potenzreihen, die im Innern des Einheitskreises beschrankt sind, J. Reine Angew. Math. vol. 147 (1917) pp. 205-232; vol. 148 (1918) pp. 122-145.
  • [7] -, Über algebraische Gleichungen, die nur Wurzeln mit negativen Realteilen besitzen, Zeitschrift für angewandte Mathematik und Mechanik vol. 1 (1921) pp. 307-311.
  • [8] H. S. Wall, Continued fraction expansions for functions with positive real parts, Bull. Amer. Math. Soc. vol. 52 (1946) pp. 138-143. MR 0015473 (7:423e)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 41.1X

Retrieve articles in all journals with MSC: 41.1X


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1947-0021626-6
Article copyright: © Copyright 1947 American Mathematical Society

American Mathematical Society