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Linear tame extension operators from closed subvarieties of $ {\bf C}\sp d$


Author: Aydın Aytuna
Journal: Proc. Amer. Math. Soc. 123 (1995), 759-763
MSC: Primary 46E10; Secondary 32C25, 46A04
DOI: https://doi.org/10.1090/S0002-9939-1995-1219717-2
MathSciNet review: 1219717
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Abstract: In this note we show that a linear continuous and tame extension operator from the space of analytic functions on a closed irreducible subvariety V of $ {\mathbb{C}^d}$ exists if and only if V is an algebraic variety.


References [Enhancements On Off] (What's this?)

  • [1] A. Aytuna, Stein spaces M for which $ \mathcal{O}(M)$ is isomorphic to a power series space, Advances in the Theory of Fréchet Spaces, Kluwer Academic Publ., Dordrecht, 1989, pp. 115-154. MR 1083561 (91m:32015)
  • [2] A. Aytuna, J. Krone, and T. Terzioglu, Complemented infinite type power series subspaces of nuclear Fréchet spaces, Math. Ann. 283 (1989), 193-202. MR 980593 (90a:46014)
  • [3] P. B. Djakov and B. S. Mitiagin, The structure of polynomial ideals in the algebra of entire functions, Studia Math. 68 (1980), 84-104. MR 583404 (82a:32006)
  • [4] R. S. Hamilton, Nash-Moser inverse function theorem, Bull. Amer. Math. Soc. (N.S.) 7 (1986), 65-222. MR 656198 (83j:58014)
  • [5] L. Hörmander, An introduction to complex analysis in several variables, North-Holland, Amsterdam, 1973.
  • [6] P. Lelong, Plurisubharmonic functions and positive differential forms, Gordon and Breach, New York, 1969.
  • [7] B. S. Mitiagin and G. M. Henkin, Linear problems of complex analysis, Russian Math. Surveys 26 (1971), 99-164. MR 0287297 (44:4504)
  • [8] W. Rudin, A geometric criterion for algebraic varieties, J. Math. Mech. 17 (1967/68), 671-683. MR 0219750 (36:2829)
  • [9] A. Sadullaev, An estimate for polynomials on analytic sets, Math. USSR-Izv. 20 (1983), 493-502.
  • [10] D. Vogt, Tame spaces and power series spaces, Math. Z. 196 (1987), 523-536. MR 917235 (89i:46005)
  • [11] -, Über die Existenz von Ausdehnungsoperatoren für holomorphe Funktionen auf analytischen Mengen in $ {C^n}$, preprint.
  • [12] V. P. Zahariuta, Isomorphisms of spaces of analytic functions, Soviet Math. Dokl. 22 (1980), 631-634.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1219717-2
Keywords: Linear tame extension operators for analytic functions defined on subvarieties of $ {\mathbb{C}^d}$, algebraic varieties
Article copyright: © Copyright 1995 American Mathematical Society

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