Nakai, Mitsuru Valuations on meromorphic functions of bounded type. (English) Zbl 0656.30026 Trans. Am. Math. Soc. 309, No. 1, 231-252 (1988). This paper contains the proofs of results described earlier in Function spaces on Riemann surfaces, Proc. Symp., Kyoto 1985, RIMS Kokyuroku 571, 122-138 (1985; Zbl 0605.30035). Reviewer: F.Forelli Cited in 1 ReviewCited in 1 Document MSC: 30D55 \(H^p\)-classes (MSC2000) Keywords:discrete valuation; bounded holomorphic functions Citations:Zbl 0605.30035 PDFBibTeX XMLCite \textit{M. Nakai}, Trans. Am. Math. Soc. 309, No. 1, 231--252 (1988; Zbl 0656.30026) Full Text: DOI References: [1] Lars V. Ahlfors, Open Riemann surfaces and extremal problems on compact subregions, Comment. Math. Helv. 24 (1950), 100 – 134. · Zbl 0041.41102 [2] Norman L. Alling, The valuation theory of meromorphic function fields, Entire Functions and Related Parts of Analysis (Proc. Sympos. Pure Math., La Jolla, Calif., 1966) Amer. Math. Soc., Providence, R.I., 1968, pp. 8 – 29. [3] Otto Endler, Valuation theory, Springer-Verlag, New York-Heidelberg, 1972. To the memory of Wolfgang Krull (26 August 1899 – 12 April 1971); Universitext. · Zbl 0257.12111 [4] F. Forelli, private communication. [5] Bent Fuglede, Sur les fonctions finement holomorphes, Ann. Inst. Fourier (Grenoble) 31 (1981), no. 4, vii, 57 – 88 (French, with English summary). · Zbl 0445.30040 [6] John B. Garnett and Peter W. Jones, The corona theorem for Denjoy domains, Acta Math. 155 (1985), no. 1-2, 27 – 40. · Zbl 0578.30043 [7] Maurice Heins, Algebraic structure and conformal mapping, Trans. Amer. Math. Soc. 89 (1958), 267 – 276. · Zbl 0083.30001 [8] Maurice Heins, Complex function theory, Pure and Applied Mathematics, Vol. 28, Academic Press, New York-London, 1968. · Zbl 1226.30001 [9] Hej Iss’sa, On the meromorphic function field of a Stein variety, Ann. of Math. (2) 83 (1966), 34 – 46. · Zbl 0146.31401 [10] Serge Lang, Algebra, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. · Zbl 0193.34701 [11] H. L. Royden, Rings of analytic and meromorphic functions, Trans. Amer. Math. Soc. 83 (1956), 269 – 276. · Zbl 0074.09801 [12] H. L. Royden, Rings of meromorphic functions, Proc. Amer. Math. Soc. 9 (1958), 959 – 965. · Zbl 0090.04901 [13] H. L. Royden, Algebras of bounded analytic functions on Riemann surfaces, Acta Math. 114 (1965), 113 – 142. · Zbl 0146.30501 [14] 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 [15] O. F. G. Schilling, The Theory of Valuations, Mathematical Surveys, No. 4, American Mathematical Society, New York, N. Y., 1950. · Zbl 0037.30702 [16] M. Tsuji, Potential theory in modern function theory, Chelsea Publishing Co., New York, 1975. Reprinting of the 1959 original. · Zbl 0322.30001 [17] Lawrence Zalcman, Bounded analytic functions on domains of infinite connectivity, Trans. Amer. Math. Soc. 144 (1969), 241 – 269. · Zbl 0188.45002 [18] Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960. · Zbl 0322.13001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.