Literature Cited
M. Szapiel and W. Szapiel, “Extreme points of convex sets (IV). Bounded typically real functions,” Bull. Acad. Pol. Sci., Sér. Sci. Math.,30, 45–57 (1982).
M. S. Robertson, “On the coefficients of typically-real functions,” Bull. Am. Math. Soc.,41, 565–572 (1935).
G. M. Goluzin, “On typically real functions,” Mat. Sb.,27, 201–218 (1950).
G. M. Goluzin, Geometric Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1966).
V. L. Goncharov, Theory of Interpolation and Approximation of Functions [in Russian], Gostekhizdat, Moscow (1954).
L. A. Lyusternik, O. A. Chervonenkis, and A. R. Yanpol'skii, Mathematical Analysis (Computation of Elementary Functions) [in Russian], Fizmatgiz, Moscow (1963).
L. D. Kudryavtsev, Mathematical Analysis [in Russian], Vol. 1, Vysshaya, Shkola, Moscow (1973).
Yu. E. Alenitsin, G. V. Kuz'mina, and N. A. Lebedev, “Methods and results of the geometric theory of functions,” in: Appendix, Geometric Theory of Functions of a Complex Variable [in Russian], G. M. Goluzin (ed.), Nauka, Moscow (1966), pp. 532–626.
C. Carathéodory, “Über den Variabilitätsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen,” Rend. Circ. Palermo,32, 193–217 (1911).
F. Riesz, “Sur certains systèmes singuliers d'équations intégrales,” Ann. sci. École norm. supér.,28, 33–62 (1911).
M. G. Krein and A. A. Nudel'man, The Markov Moments Problem and Extremal Problems [in Russian], Nauka, Moscow (1973).
M. Berge, Geometry [Russian translation], Vol 1, Mir, Moscow (1984).
V. G. Boltyanskii, Optimal Control of Discrete Systems [in Russian], Nauka, Moscow (1973).
Mathematical Encyclopedia [in Russian], Vol. 1, Sovetskii, Entsiklopediya, Moscow (1977).
W. Blaschke, Disks and Balls [Russian translation], Nauka, Moscow (1967).
I. M. Yaglom and V. G. Boltyanskii, Convex Figures [in Russian], Gostekhizdat, Moscow-Leningrad (1951).
V. G. Boltyanskii and I. M. Yaglom, “Convex figures and bodies,” in: Encyclopedia of Elementary Mathematics [in Russian], Vol. V. Geometry, Nauka, Moscow (1966), pp. 181–269.
B. Grünbaum, “Measures of symmetry for convex sets,” in: Convexity, Proc. Sympos. Purs Math., Vol. 7, Am. Math Soc., Providence (1963), pp. 233–270.
V. V. Chernikov, “Estimates of coefficients with constraints in the class of typicallay real functions in the disk,” Mat. Zametki,37, 337–344 (1985).
Additional information
Tomsk. Translated from Sibirskii Mathematicheskii Zhurnal, Vol. 31, No. 2, pp. 191–196, March–April, 1990.
Rights and permissions
About this article
Cite this article
Chernikov, V.V. Domains of values of systems of coefficients of bounded typically real functions in the disk. Sib Math J 31, 345–350 (1990). https://doi.org/10.1007/BF00970665
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00970665