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Literature Cited
V. P. Khavin, “Space of analytic functions,” in: Mathematical Analysis 1964 [in Russian], Itogi Nauki, VINITI, Moscow (1966), pp. 76–164.
L. A. Rubel and B. A. Taylor, “Functional analysis proofs of some theorems in function theory,” Am. Math. Mon., No. 5, 483–488 (1969).
G. Köthe, “Dualität in der Funktionentheorie,” J. Reine Angew. Math.,191, 30–49 (1953).
A. Grothendieck, “Sur certains espaces de fonctions holomorphes. I, II,” J. Reine Angew. Math.,192, No. 1, 35–64; No. 2, 77–95 (1953).
J. Sebastiao e Silva, “As funcoes analiticas e analyse functional,” Portugal. Math.,9, 1–130 (1950).
V. P. Khavin, “Separation of singularities of analytic functions,” Dokl. Akad. Nauk SSSR,121, No. 2, 239–248 (1958).
P. Levy, Concrete Problems of Functional Analysis [in Russian], Nauka, Moscow (1967).
H. G. Tillman, “Randwertverteilungen und analytischer Funktionen und Distributionen,” Math. Z.,59, 61–83 (1953).
A. Martineau, “Sur les equations aux derivees partielles a coefficients constants avec second membre, dans le champ complexe,” C. R. Acad. Sci.,264, 400–401 (1967).
A. Martineau, “Sur la notion d'ensemble fortement lineelement convexe,” Anais Acad. Brasill. Cienc.,4, No. 4, 427–435 (1968).
A. Martineau, “Equations differentielles d'ordre infini,” Bull. Soc. Math. France,95, 109–154 (1967).
Andre Martineau, Oeuvres, CNRE, Paris (1977).
L. A. Aizenberg, “Linear convexity inC n and separation of singularities of holomorphic functions,” Bull. Acad. Polon. Sci. Ser. Math.,15, No. 7, 487–495 (1967).
L. A. Aizenberg, “Expansion of holomorphic functions of several variables in partial fractions,” Sib. Mat. Zh.,8, No. 5, 1124–1142 (1967).
V. M. Trutnev, “Analogue of Laurent series for functions of several complex variables, holomorphic on strongly linearly convex sets,” in: Holomorphic Functions of Several Complex Variables [in Russian], IF Sib. Otd. Akad. Nauk SSSR, Krasnoyarsk (1972), pp. 139–152.
V. M. Trutnev, “Properties of functions, holomorphic on strongly linear convex sets,” in: Some Properties of Holomorphic Functions of Several Complex Variables [in Russian], IF Sib. Otd. Akad. Nauk SSSR, Krasnoyarsk (1973), pp. 139–155.
L. A. Aizenberg, “General form of a continuous linear functional on spaces of functions, holomorphic in convex domains inC n,” Dokl. Akad. Nauk SSSR,166, No. 5, 1015–1018 (1966).
A. P. Yuzhakov and V. P. Krivokolesko, “Linearly convex domains with smooth boundaries inC n,” Sib. Mat. Zh.,12, No. 2, 452–458 (1971).
L. A. Aizenberg, “Linear functionals on spaces of analytic functions and linear convexity inC n,” Investigations on Linear Operators and the Theory of Functions. 99 Unsolved Problems of Linear and Complex Analysis, J. Sov. Math.,26, No. 5 (1984).
S. V. Znamenskii, “Geometric tests for strong linear convexity,” Funkts. Anal.,13, No. 3, 83–84 (1979).
A. Martineau, “Sur la topologie des espaces de fonctions holomorphes,” Math. Ann.,163, No. 1, 62–88 (1966).
B. V. Shabat, Introduction to Complex Analysis [in Russian], Part 2, Nauka, Moscow (1976).
Additional information
Krasnoyarsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 26, No. 3, pp. 31–43, May–June, 1985.
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Znamenskii, S.V. Strong linear convexity. I. Duality of spaces of holomorphic functions. Sib Math J 26, 331–341 (1985). https://doi.org/10.1007/BF00968619
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DOI: https://doi.org/10.1007/BF00968619