Constants are definable in rings of analytic functions
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- by Taneli Huuskonen PDF
- Proc. Amer. Math. Soc. 122 (1994), 697-702 Request permission
Abstract:
The analytic functions defined in a fixed domain form a ring with pointwise addition and multiplication. We describe a way to define constants in the ring using a first-order formula which is independent of the domain.References
- Lipman Bers, On rings of analytic functions, Bull. Amer. Math. Soc. 54 (1948), 311–315. MR 24970, DOI 10.1090/S0002-9904-1948-08992-3
- Joseph Becker, C. Ward Henson, and Lee A. Rubel, First-order conformal invariants, Ann. of Math. (2) 112 (1980), no. 1, 123–178. MR 584077, DOI 10.2307/1971323
- G. M. Goluzin, Geometric theory of functions of a complex variable, Translations of Mathematical Monographs, Vol. 26, American Mathematical Society, Providence, R.I., 1969. MR 0247039
- Taneli Huuskonen, The construction of a definable noncategorical domain, Z. Math. Logik Grundlag. Math. 37 (1991), no. 3, 217–226. MR 1155393, DOI 10.1002/malq.19910371305 P. Montel, Leçons sur les familles normales de fonctions analytiques et leurs applications, Gauthier-Villars, Paris, 1927.
- Lee A. Rubel, On the ring of differentially-algebraic entire functions, J. Symbolic Logic 57 (1992), no. 2, 449–451. MR 1169181, DOI 10.2307/2275279
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 697-702
- MSC: Primary 16S60; Secondary 03C40, 03C60, 30C35
- DOI: https://doi.org/10.1090/S0002-9939-1994-1204378-8
- MathSciNet review: 1204378