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

Frank, Evelyn

doi:10.1090/S0002-9947-1947-0021626-6

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

Herbert Bilharz, Bemerkung zu einem Satze von Hurwitz, Z. Angew. Math. Mech. 24 (1944), 77–82 (German). MR 12710, DOI https://doi.org/10.1002/zamm.19440240205
C. Carathéodory, Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen, Math. Ann. 64 (1907), no. 1, 95–115 (German). MR 1511425, DOI https://doi.org/10.1007/BF01449883
Evelyn Frank, On the zeros of polynomials with complex coefficients, Bull. Amer. Math. Soc. 52 (1946), 144–157. MR 14509, DOI https://doi.org/10.1090/S0002-9904-1946-08526-2
Evelyn Frank, The location of the zeros of polynomials with complex coefficients, Bull. Amer. Math. Soc. 52 (1946), 890–898. MR 17440, DOI https://doi.org/10.1090/S0002-9904-1946-08668-1
J. Geronimus, On polynomials orthogonal on the circle, on trigonometric moment-problem and on allied Carathéodory and Schur functions, Rec. Math. [Mat. Sbornik] N. S. 15(57) (1944), 99–130 (Russian., with English summary). MR 0012715

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.

---, Über algebraische Gleichungen, die nur Wurzeln mit negativen Realteilen besitzen, Zeitschrift für angewandte Mathematik und Mechanik vol. 1 (1921) pp. 307-311.

H. S. Wall, Continued fraction expansions for functions with positive real parts, Bull. Amer. Math. Soc. 52 (1946), 138–143. MR 15473, DOI https://doi.org/10.1090/S0002-9904-1946-08525-0