Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Holomorphic approximation on compact, holomorphically convex, real-analytic varieties


Author: Edgar Lee Stout
Journal: Proc. Amer. Math. Soc. 134 (2006), 2303-2308
MSC (2000): Primary 32E30
Posted: February 2, 2006
MathSciNet review: 2213703
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Every continuous function on a compact, holomorphically convex, real-analytic subset of $ \mathbb{C}^N$ can be approximated uniformly by functions holomorphic on the set.


References

  • 1. P. Ahern and W. Rudin, Totally real embeddings of $ S\sp 3$ in $ {\bf C}\sp 3$, Proc. Amer. Math. Soc., 94, 1985, pp. 460-462. MR 0787894 (86g:32031)
  • 2. J.T. Anderson, A. Izzo, and J. Wermer, Polynomial approximation on real-analytic varieties in $ {\bf C}\sp n$, Proc. Amer. Math. Soc., 132, 2004, pp. 1495-1500. MR 2053357 (2005d:32017)
  • 3. F.T. Birtel, Some holomorphic function algebras, Papers from the Summer Gathering on Function Algebras (Aarhus, 1969), pp. 11-18. Matematisk Inst., Aarhus Univ., Aarhus, 1969. MR 0254598 (40:7806)
  • 4. F.T. Birtel, Algebras of Holomorphic Functions: 40 Lectures, Tulane University Mathematics Department, New Orleans, 1972.
  • 5. J.-E. Björk, Holomorphic convexity and analytic structures in Banach algebras, Ark. Mat.,(9), 1971, pp. 39-54. MR 0385170 (52:6035)
  • 6. K. Diederich and J.-E. Fornæss, Pseudoconvex domains with real-analytic boundary, Ann. Math. (2), (107), 1978, pp. 371-384. MR 0477153 (57:16696)
  • 7. J. Duval and N. Sibony, Polynomial convexity, rational convexity, and currents, Duke Math. J., (79), 1995, pp. 487-513. MR 1344768 (96f:32016)
  • 8. F.R. Harvey and R.O. Wells, Jr., Compact holomorphically convex subsets of a Stein manifold, Trans. Amer. Math. Soc., (136), 1969, pp. 509-516. MR 0235158 (38:3470)
  • 9. F.R. Harvey and R.O. Wells, Jr., Holomorphic approximation and hyperfunction theory on a $ {C}\sp{1}$ totally real submanifold of a complex manifold, Math. Ann., (197), 1972, pp. 287-318. MR 0310278 (46:9379)
  • 10. C.D. Hill and G. Taiani, Families of analytic discs in $ {\bf C}\sp{n}$ with boundaries on a prescribed CR submanifold, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), (5) 1978, pp. 327-380. MR 0501906 (80c:32023)
  • 11. A.J. Izzo, Failure of polynomial approximation on polynomially convex subsets of the sphere, Bull. London Math. Soc., (28) 1996, 393-397. MR 1384828 (98d:32017)
  • 12. R. Narasimhan, Introduction to the Theory of Analytic Spaces, Springer Lecture Notes in Mathematics, vol. 25, Springer-Verlag, Berlin, Heidelberg, New York, 1966. MR 0217337 (36:428)
  • 13. A.G. O'Farrell, K.J. Preskenis, and D. Walsh, Holomorphic approximation in Lipschitz norms, Proceedings of the conference on Banach algebras and several complex variables (New Haven, Conn., 1983), Contemp. Math., (32), 187-194. Amer. Math. Soc., Providence, RI, 1984. MR 0769507 (86c:32015)
  • 14. P.J. de Paepe, Homomorphism spaces of algebras of holomorphic functions, Pacific J. Math., (66), 1976, pp. 211-220. MR 0442282 (56:668)
  • 15. A. Selvaggi Primicerio, and G. Taiani, Famiglie di dischi analitici con bordo su sottovarietà CR non generiche, Ann. Mat. Pura Appl. (4), (126), 1980, pp. 233-251. MR 0612361 (82j:32047)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32E30

Retrieve articles in all journals with MSC (2000): 32E30


Additional Information

Edgar Lee Stout
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
Email: stout@math.washington.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08250-5
PII: S 0002-9939(06)08250-5
Keywords: Holomorphic approximation, holomorphically convex sets.
Received by editor(s): June 8, 2004
Received by editor(s) in revised form: March 2, 2005
Posted: February 2, 2006
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2006 American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia