Local holomorphic extendability and non-extendability of C R -functions on smooth boundaries

John Erik Fornæss; Claudio Rea

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1985)

  • Volume: 12, Issue: 3, page 491-502
  • ISSN: 0391-173X

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Fornæss, John Erik, and Rea, Claudio. "Local holomorphic extendability and non-extendability of $CR$-functions on smooth boundaries." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 12.3 (1985): 491-502. <http://eudml.org/doc/83964>.

@article{Fornæss1985,
author = {Fornæss, John Erik, Rea, Claudio},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {local extendability of CR-functions; rays condition; local peak point},
language = {eng},
number = {3},
pages = {491-502},
publisher = {Scuola normale superiore},
title = {Local holomorphic extendability and non-extendability of $CR$-functions on smooth boundaries},
url = {http://eudml.org/doc/83964},
volume = {12},
year = {1985},
}

TY - JOUR
AU - Fornæss, John Erik
AU - Rea, Claudio
TI - Local holomorphic extendability and non-extendability of $CR$-functions on smooth boundaries
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1985
PB - Scuola normale superiore
VL - 12
IS - 3
SP - 491
EP - 502
LA - eng
KW - local extendability of CR-functions; rays condition; local peak point
UR - http://eudml.org/doc/83964
ER -

References

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  1. [1] M.S. Baouendi - F. Treves, About the holomorphic extension fo CR-functions on real hypersurfaces in complex space, Duke Math. J., 51 (1984), pp. 77-107. Zbl0564.32011MR744289
  2. [2] E. Bedford, Local and global envelopes of holomorphy of domains in C2. (Preprint). Zbl0599.32010
  3. [3] E. Bedford - J.E. Fornæss, Local extension of CR-functions from weakly pseudoconvex boundaries, Michigan Math. J., 25 (1978) pp. 259-262. Zbl0401.32007MR512898
  4. [4] E. Bedford and J.E. Fornæss, A construction of peak functions on weakly pseudoconvex domains, Ann. of Math., 107 (1978), pp. 555-568. Zbl0392.32004MR492400
  5. [5] C.O. Kiselman, On entire functions of exponential type and indicators of analytic functionals, Acta Math.117, (1967), pp. 1-35. Zbl0152.07602MR210940
  6. [6] J.J. Kohn - L. Nirenberg, A pseudoconvex demain not admitting a holomorphic support function, Math. Ann.201 (1973), pp. 265-268. Zbl0248.32013MR330513
  7. [7] E.E. Levi, Sulle ipersurperfici dello spazio a 4 dimensioni che possono essere frontiera del campo di esistenza di una funzione analitica di due variabili complesse, Ann. Mat. Pura Appl., 18, s. III (1911), pp. 69-79. Zbl42.0449.02JFM42.0449.02
  8. [8] H. Lewy, On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables, Ann. of Math., 74 (1956), pp. 514-522. Zbl0074.06204MR81952
  9. [9] C. Rea, Extension holomorphe bilatérale des fonctions de Cauchy-Riemann données sur une hypersurface différentiable de C2, C. R. Acad. Sc. Paris, Sér. A, 294, (1982), pp. 577-579. Zbl0496.32013MR663083
  10. [10] C. Rea, The Cauchy problem for the ∂ operator, Boll. UMI (6), 1-A (1982), pp. 443-449. Zbl0525.32018
  11. [11] C. Rea, Prolongement holomorphe des fonctions CR, conditions suffisantes, C. R. Acad. Sc. Paris, 297 (1983), pp. 163-166. Zbl0568.32011MR725396
  12. [12] L.I. Ronkin, Introduction to the theory of entire functions of several variables, Tr. of Math. Monographs, 44, A.M.S. (1974). Zbl0286.32004MR346175
  13. [13] B. Stensønes- Henriksen, Ph. D. Thesis, Princeton University. 
  14. [14] A. Bogges - J. Pitts, CR extension near a point of higher type, Duke Math. J., 52 (1985), pp. 67-102. Zbl0573.32019MR791293

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