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Literature Cited
E. Borel. Leçons sur les Séries a Termes Positifs. Paris (1902).
G. Valiron, Sur un Théorème de M. Hadamard, Bull. Sci. Math.,47, No. 1, 177–192 (1923).
P. Lelong, Sur Quelques Problèmes de la Théorie des Fonctions de Deux Variables Complexes, Ann. Sci. Ecole Norm. Sup.,58, 83–177 (1948).
A. A. Gol'dberg, Elementary Remarks on Formulas for the Definition of Order and Type for Entire Functions of Many Variables. Dokl. Akad. Nauk ArmSSR.29, No. 4, 145–151 (1959).
A. A. Gol'dberg, Formulas for the Definition of Order and Type for Entire Functions of Many Variables. Dokl. i Soobshch. Uzhgorodskogo Un-ta, Seriya Fiz. Matem. Nauk, No. 4, 101–103 (1961).
M. M. Dzhrbashyan, A Theory of Classes of Entire Functions of Many Variables, Izv. Akad. Nauk of the Armenian SSR, Seriya Fiz. Matem. Nauk. Est. i Tekhn. Nauk,8, No. 4, 1–23 (1955).
L. I. Ronkin, The Associated Orders and Types of Entire Functions of Many Variables, Ukr. Matem. Zh.,14, No. 3, 408–413 (1964).
L. I. Ronkin, The Growth of the Function Φ(r1.....rn). Convex with Respect to In r1, ..., In rn, Dokl. Akad. Nauk SSSR,172, No. 5, 1028–1031 (1967).
Sh. I. Strelits, The Behavior of an Entire Transcendental Function by Its Maximum Modulus, Litovsk. Matem. Sb.,4, No. 3, 357–408 (1964).
B. A. Fuks, An Introduction to the Theory of Analytic Functions of Many Complex Variables [in Russian], Fizmatgiz, Moscow (1962).
D. A. Raikov, Vector Spaces [in Russian], Fizmatgiz, Moscow (1962).
F. A. Valentine, Convex Sets, New York (1963).
H. G. Eggleston, Convexity, Cambridge (1958).
H. Minkowski, Theorie der convexen Körper, ins besondere Begründung ihres Oberflachenbegriffs, Ges. Abh.,25, 131–229 (1911).
S. Gass, Linear Programming, Fizmatgiz, Moscow (1961).
A. J. Goldman and A. C. Tucker, Polyhedral Convex Cones, in: Linear Inequalities and Mixed Problems [Russian translation], IL, Moscow (1959), pp. 142–161.
N. Burbaki, Functions of a Real Variable [in Russian], Izd. Nauka, Moscow (1965).
V. S. Vladimirov, Methods in the Theory of Functions of Many Complex Variables [in Russian], Nauka Moscow (1964).
L. S. Maergroiz, The Question of Characterizing the Growth of Entire Functions of Many Variables, Uch. Zap. Mosk. Obl., Ped. In-ta,137, 133–149 (1964).
L. S. Macrgroiz, The Questions of the Connection between the Different Orders of Growth of Entire Functions of Many Variables, Sib. Matem. Zh.,7, No. 6, 1268–1292 (1966).
R. T. Rockefeller, Level Sets and Continuity of Conjugate Convex Functions, Trans. Amer. Math. Soc.,123, No. 1, 46–63 (1966).
R. A. Wijsman, Convergence of Sequences of Convex Sets, Cones and Functions, Trans. Amer. Math. Soc.,123, No. 1, 32–45 (1966).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 9, No. 3, pp. 577–591, May–June, 1968.
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Macrgroiz, L.S. Properties of convex sets and their applications to the theory of growth of convex and entire functions. Sib Math J 9, 435–444 (1968). https://doi.org/10.1007/BF01040906
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DOI: https://doi.org/10.1007/BF01040906