The space of bounded analytic functions on a region
Annales de l'Institut Fourier, Volume 16 (1966) no. 1, pp. 235-277.

L’espace des fonctions analytiques bornées sur une région peut être muni de plusieurs topologies différentes. Deux topologies faibles sont étudiées ici. L’une est celle appelée topologie stricte et l’autre la topologie faible étoilée. Le principal outil nouveau est une espèce de balayage ou ramonage.

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     volume = {16},
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Rubel, Lee A.; Shields, A. L. The space of bounded analytic functions on a region. Annales de l'Institut Fourier, Volume 16 (1966) no. 1, pp. 235-277. doi : 10.5802/aif.231. https://aif.centre-mersenne.org/articles/10.5802/aif.231/

[1] L. Ahlfors and L. Sario, Riemann Surfaces, Princeton (1960). | MR: 22 #5729 | Zbl: 0196.33801

[2] S. Banach, Théorie des Opérations Linéaires, Warszawa-Lwow (1932). | JFM: 58.0420.01 | Zbl: 0005.20901

[3] A. Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math., 81 (1949), 239-255. | MR: 10,381e | Zbl: 0033.37701

[4] L. Brown, A. L. Shields and K. Zeller, On absolutely convergent exponential sums, Trans. Amer. Math. Soc., 96 (1960), 162-183. | MR: 26 #332 | Zbl: 0096.05103

[5] R. C. Buck, Algebraic properties of classes of analytic functions, Seminars on Analytic Functions, vol. II, Princeton (1957), 175-188. | Zbl: 0196.43603

[6] L. Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547-559. | MR: 25 #5186 | Zbl: 0112.29702

[7] L. Carleson, On bounded analytic functions and closure problems, Ark. Mat. 2 (1952), 283-291. | MR: 14,630d | Zbl: 0047.35301

[8] H. Cartan, Elementary Theory of Analytic Functions of One or Several Complex Variables, Paris (1963). | MR: 27 #4911 | Zbl: 0121.30501

[9] N. Dunford and J. Schwartz, Linear Operators, Part I, New York (1958). | MR: 22 #8302 | Zbl: 0084.10402

[10] V. P. Havin, On the space of bounded regular functions, Sibirsk. Mat. Z., 2 (1961), 622-638 (See also the abstract, under the same title, Dokl. Adak. Nauk SSSR, 131 (1960), 40-43, translated in Soviet Math., 1 (1960), 202-204). | Zbl: 0174.12003

[11] O. Helmer, Divisibility properties of integral functions, Duke Math. J., 6 (1940), 38-47. | JFM: 66.0105.02 | Zbl: 0023.23904

[12] H. Helson, Lectures on Invariant Subspaces, New York (1964). | MR: 30 #1409 | Zbl: 0119.11303

[13] E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc. Colloquium Publications, 31 (1957). | MR: 19,664d | Zbl: 0078.10004

[14] K. Hoffman, Banach Spaces of Analytic Functions, Englewood Cliffs (1962). | MR: 24 #A2844 | Zbl: 0117.34001

[15] J. L. Kelley, General Topology, New York (1955). | MR: 16,1136c | Zbl: 0066.16604

[16] J. L. Kelley, I. Namioka et al., Linear Topological Spaces, Princeton (1963). | MR: 29 #3851 | Zbl: 0115.09902

[17] K. De Leeuw and W. Rudin, Extreme points and extremum problems in H1, Pacific J. Math., 8 (1958), 467-485. | MR: 20 #5426 | Zbl: 0084.27503

[18] E. Michael, Locally Multiplicatively-convex Topological Algebras, Mem. Amer. Math. Soc., 11 (1952). | MR: 14,482a | Zbl: 0047.35502

[19] W. W. Rogosinski and H. S. Shapiro, On certain extremum problems for analytic functions, Acta. Math., 90 (1953), 287-318. | MR: 15,516a | Zbl: 0051.05604

[20] L. A. Rubel and A. L. Shields, Bounded approximation by polynomials, Acta Math., 112 (1964), 145-162. | MR: 30 #5104 | Zbl: 0136.37404

[21] L. A. Rubel and A. L. Shields, Weak topologies on the bounded holomorphic functions, Bull. Amer. Math. Soc. (1965). | MR: 30 #2364 | Zbl: 0135.16903

[22] W. Rudin, Essential boundary points, Bull. Amer. Math. Soc. 70 (1964), 321-324. | MR: 28 #3167 | Zbl: 0133.03605

[23] A. E. Taylor, Banach spaces of functions analytic in the unit circle II, Studia Math., 12 (1951), 25-50. | MR: 13,252a | Zbl: 0042.35703

[24] J. Wolff, Sur les séries Σ Ak/z — αk, C. R. Acad. Sci. Paris, 173 (1921), 1057-1058, 1327-1328. | JFM: 48.0320.01

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