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Journal of Mathematical Sciences

, Volume 150, Issue 3, pp 2005–2012 | Cite as

On a region of values in the class of typically real functions

  • E. G. Goluzina
Article
  • 18 Downloads

Abstract

The paper studies the regions of values of the systems {f(z1), f(r1), f(r2),…, f(rn)} and {f(r1), f(r2),…, f (rn)}, where n ⁥ 2; z1 is an arbitrary fixed point of the disk U = {z: |z| < 1} with Im z1 ≠ 0; rj are fixed numbers, 0 < rj < 1, j = 1, 2,…, n; f ∈ T, and the class T consists of the functions f(z), f(0) = 0, f′(0) = 1, regular in the disk U and satisfying the condition Im f(z) · Imz > 0 for Im z ≠ 0. As an implication, the region of values of f(z1) in the subclass of functions f ∈ T with prescribed values f(rj) (j = 1, 2,…, n) is determined. Bibliography: 12 titles.

Keywords

Russia Real Function 
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References

  1. 1.
    E. G. Goluzina, “The region of values of the system {f(z 1),…, f(z n)} in the class of typically real functions. III,” Zap. Nauchn. Semin. POMI, 337, 23–31 (2000).Google Scholar
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    E. G. Goluzina, “The region of values of the system {f(z 1), f(z 2), f(z 3)} on the class of typically real functions,” Zap. Nauchn. Semin. POMI, 302, 5–17 (2003).MathSciNetGoogle Scholar
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    M. S. Robertson, “On the coefficients of a typically-real function,” Bull. Amer. Math. Soc., 41, No. 8, 565–572 (1935).MATHCrossRefGoogle Scholar
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    G. M. Goluzin, “On typically real functions,” Mat. Sb., 27(69), No. 2, 201–218 (1950).MathSciNetGoogle Scholar
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    M. G. Krein and A. A. Nudelman, Markov’s Moment Problem and Extremal Problems [in Russian], Moscow (1973).Google Scholar
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    E. G. Goluzina, “The region of values of the system {f(z 1),…, f(z n)} in the class of typically real functions,” Zap. Nauchn. Semin. POMI, 314, 41–51 (2001).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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