Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Higher order analogues to the tangential Cauchy-Riemann equations for real submanifolds of $ {\bf C}\sp{n}$ with C.R. singularity


Author: Gary Alvin Harris
Journal: Proc. Amer. Math. Soc. 74 (1979), 79-86
MSC: Primary 32F25; Secondary 32C05
DOI: https://doi.org/10.1090/S0002-9939-1979-0521877-4
MathSciNet review: 521877
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An infinite succession of higher order operators are developed for real $ {\mathcal{C}^\infty }$ submanifolds of $ {C^n}$, with possible C.R. singularity, which reduce to the tangential Cauchy-Riemann operator in the case of a C.R. submanifold. Certain known holomorphic approximation and extension results for C.R. submanifolds are then ``extended'' to the non-C.R. case.


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

  • [1] P. Eakin and G. Harris, When $ \Phi (f)$ convergent implies f is convergent, Math. Ann. 229 (1977), 211-221. MR 0444651 (56:3001)
  • [2] M. Freeman, Tangential Cauchy-Riemann equations and uniform approximation, Pacific J. Math. 33 (1970), 101-108. MR 0264117 (41:8713)
  • [3] S. Greenfield, Cauchy-Riemann equations in several variables, Ann. Scuola Norm. Sup. Pisa 22 (1968), 275-314. MR 0237816 (38:6097)
  • [4] G. Harris, The traces of holomorphic functions on real submanifolds, Trans. Amer. Math. Soc. 242 (1978), 205-223. MR 0477120 (57:16664)
  • [5] C. D. Hill, A Kontinuitätssatz for $ {\bar \partial _M}$ and Lewy extendibility, Indiana Univ. Math. J. 22 (1972/73), 339-353. MR 0304699 (46:3831)
  • [6] L. Hormander and J. Wermer, Uniform approximation on compact subsets in $ {C^n}$, Math. Scand. 23 (1968), 5-21. MR 0254275 (40:7484)
  • [7] R. Nirenberg and R. O. Wells, Jr., Approximation theorems on differentiate submanifolds of a complex manifold, Trans. Amer. Math. Soc. 142 (1969), 15-35. MR 0245834 (39:7140)
  • [8] G. Tomassim, Tracce delle funzioni olomorfe sulle sottovarietà analitiche reali d'una varietà complessa, Ann. Scuola Norm. Sup. Pisa (3) 20 (1966), 31-43. MR 0206992 (34:6808)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32F25, 32C05

Retrieve articles in all journals with MSC: 32F25, 32C05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0521877-4
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society