On a class of ∂ ¯ -equations without solutions

Telemachos Hatziafratis

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 3, page 503-509
  • ISSN: 0010-2628

Abstract

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In this note we construct ∂ ¯ -equations (inhomogeneous Cauchy-Riemann equations) without solutions. The construction involves Bochner-Martinelli type kernels and differentiation with respect to certain parameters in appropriate directions.

How to cite

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Hatziafratis, Telemachos. "On a class of $\overline{\partial }$-equations without solutions." Commentationes Mathematicae Universitatis Carolinae 39.3 (1998): 503-509. <http://eudml.org/doc/248227>.

@article{Hatziafratis1998,
abstract = {In this note we construct $\overline\{\partial \}$-equations (inhomogeneous Cauchy-Riemann equations) without solutions. The construction involves Bochner-Martinelli type kernels and differentiation with respect to certain parameters in appropriate directions.},
author = {Hatziafratis, Telemachos},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\overline\{\partial \}$-equation; Bochner-Martinelli type kernels; -equation; Bochner-Martinelli type kernels},
language = {eng},
number = {3},
pages = {503-509},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a class of $\overline\{\partial \}$-equations without solutions},
url = {http://eudml.org/doc/248227},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Hatziafratis, Telemachos
TI - On a class of $\overline{\partial }$-equations without solutions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 3
SP - 503
EP - 509
AB - In this note we construct $\overline{\partial }$-equations (inhomogeneous Cauchy-Riemann equations) without solutions. The construction involves Bochner-Martinelli type kernels and differentiation with respect to certain parameters in appropriate directions.
LA - eng
KW - $\overline{\partial }$-equation; Bochner-Martinelli type kernels; -equation; Bochner-Martinelli type kernels
UR - http://eudml.org/doc/248227
ER -

References

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  1. Aizenberg I., Yuzhakov A., Integral representations in multidimensional complex analysis, Trans. Math. Monos., vol. 58, Amer. Math. Soc., Providence, R.I., 1983. MR0735793
  2. Gunning R., Introduction to Holomorphic Functions of Several Variables, Vol. III, Wadsworth and Brooks/Cole, 1990. Zbl0699.32001MR1059457
  3. Hatziafratis T., Integral representation formulas on analytic varieties, Pacific J. Math. 123 (1986), 71-91. (1986) Zbl0591.32003MR0834139
  4. Henkin G.M., Leiterer J., Andreotti-Grauert Theory by Integral Formulas, Birkhauser, 1988. Zbl0654.32002MR0986248
  5. Kytmanov A., The Bochner-Martinelli Integral and its Applications, Birkhauser, 1995. Zbl0834.32001MR1409816
  6. Rudin W., Function Theory in the Unit Ball of ℂ n , Springer-Verlag, 1980. MR0601594

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