Bounded analytic functions on two sheeted discs. (English) Zbl 0759.30018
Author’s abstract: Results of qualitative nature of both positive and negative directions on the point separation by bounded analytic functions of smooth subregions of two sheeted discs are given when two sheeted discs themselves are not separated by bounded analytic functions. We are, in particular, concerned about roles of branch points in two sheeted discs played in the point separation by bounded analytic functions.
Reviewer: H.Köditz (Hannover)
MSC:
| 30F20 | Classification theory of Riemann surfaces |
| 30D50 | Blaschke products, etc. (MSC2000) |
| 30D55 | \(H^p\)-classes (MSC2000) |
| 46J10 | Banach algebras of continuous functions, function algebras |
References:
| [1] | Stephen D. Fisher, Function theory on planar domains, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1983. A second course in complex analysis; A Wiley-Interscience Publication. · Zbl 0511.30022 |
| [2] | Frank Forelli, A note on divisibility in \?^{\infty }(\?), Canad. J. Math. 36 (1984), no. 3, 458 – 469. · Zbl 0567.30023 · doi:10.4153/CJM-1984-028-7 |
| [3] | John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. · Zbl 0469.30024 |
| [4] | Mikihiro Hayashi and Mitsuru Nakai, Point separation by bounded analytic functions of a covering Riemann surface, Pacific J. Math. 134 (1988), no. 2, 261 – 273. · Zbl 0627.30031 |
| [5] | Kiyoshi Niino , Analytic function theory of one complex variable, Pitman Research Notes in Mathematics Series, vol. 212, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989. · Zbl 0676.00009 |
| [6] | P. J. Myrberg, Über die analytische Fortsetzung von beschränkten Funktionen, Ann. Acad. Sci. Fennicae. Ser. A. I. Math.-Phys. 1949 (1949), no. 58, 7 (German). · Zbl 0034.05203 |
| [7] | H. L. Royden, Algebras of bounded analytic functions on Riemann surfaces, Acta Math. 114 (1965), 113 – 142. · Zbl 0146.30501 · doi:10.1007/BF02391819 |
| [8] | L. Sario and M. Nakai, Classification theory of Riemann surfaces, Die Grundlehren der mathematischen Wissenschaften, Band 164, Springer-Verlag, New York-Berlin, 1970. · Zbl 0199.40603 |
| [9] | Shigeo Segawa, Bounded analytic functions on unbounded covering surfaces, Pacific J. Math. 79 (1978), no. 1, 183 – 187. · Zbl 0405.30036 |
| [10] | Henrik L. Selberg, Ein Satz über beschränkte endlichvieldeutige analytische Funktionen, Comment. Math. Helv. 9 (1936), no. 1, 104 – 108 (German). · Zbl 0015.30805 · doi:10.1007/BF01258178 |
| [11] | Charles M. Stanton, Bounded analytic functions on a class of open Riemann surfaces, Pacific J. Math. 59 (1975), no. 2, 557 – 565. · Zbl 0328.30040 |
| [12] | M. Tsuji, Potential theory in modern function theory, Chelsea Publishing Co., New York, 1975. Reprinting of the 1959 original. · Zbl 0322.30001 |
| [13] | Yoshikatsu Yamamura, On the existence of bounded analytic functions, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 10 (1969), 88 – 102 (1969). · Zbl 0175.36302 |
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