Zeroes of the Bergman kernel of Hartogs domains

Miroslav Engliš

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 1, page 199-202
  • ISSN: 0010-2628

Abstract

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We exhibit a class of bounded, strongly convex Hartogs domains with real-analytic boundary which are not Lu Qi-Keng, i.e. whose Bergman kernel function has a zero.

How to cite

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Engliš, Miroslav. "Zeroes of the Bergman kernel of Hartogs domains." Commentationes Mathematicae Universitatis Carolinae 41.1 (2000): 199-202. <http://eudml.org/doc/248643>.

@article{Engliš2000,
abstract = {We exhibit a class of bounded, strongly convex Hartogs domains with real-analytic boundary which are not Lu Qi-Keng, i.e. whose Bergman kernel function has a zero.},
author = {Engliš, Miroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Lu Qi-Keng conjecture; Hartogs domain; Bergman kernel; Lu Qi-Keng conjecture; Hartogs domain; Bergman kernel},
language = {eng},
number = {1},
pages = {199-202},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Zeroes of the Bergman kernel of Hartogs domains},
url = {http://eudml.org/doc/248643},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Engliš, Miroslav
TI - Zeroes of the Bergman kernel of Hartogs domains
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 1
SP - 199
EP - 202
AB - We exhibit a class of bounded, strongly convex Hartogs domains with real-analytic boundary which are not Lu Qi-Keng, i.e. whose Bergman kernel function has a zero.
LA - eng
KW - Lu Qi-Keng conjecture; Hartogs domain; Bergman kernel; Lu Qi-Keng conjecture; Hartogs domain; Bergman kernel
UR - http://eudml.org/doc/248643
ER -

References

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  1. Boas H.P., Counterexample to the Lu Qi-Keng conjecture, Proc. Amer. Math. Soc. 97 (1986), 374-375. (1986) Zbl0596.32032MR0835902
  2. Boas H.P., The Lu Qi-Keng conjecture fails generically, Proc. Amer. Math. Soc. 124 (1996), 2021-2027. (1996) Zbl0857.32010MR1317032
  3. Boas H.P., Fu S., Straube E., The Bergman kernel function: explicit formulas and zeroes, Proc. Amer. Math. Soc. 127 (1999), 805-811. (1999) Zbl0919.32013MR1469401
  4. Engliš M., Asymptotic behaviour of reproducing kernels of weighted Bergman spaces, Trans. Amer. Math. Soc. 349 (1997), 3717-3735. (1997) MR1401769
  5. Engliš M., A Forelli-Rudin construction and asymptotics of weighted Bergman kernels, preprint, 1998. MR1795632
  6. Ligocka E., On the Forelli-Rudin construction and weighted Bergman projections, Studia Math. 94 (1989), 257-272. (1989) Zbl0688.32020MR1019793
  7. Lu Q.-K. (K.H. Look), On Kaehler manifolds with constant curvature, Chinese Math. 8 (1966), 283-298. (1966) MR0206990
  8. Oeljeklaus K., Pflug P., Youssfi E.H., The Bergman kernel of the minimal ball and applications, Ann. Inst. Fourier (Grenoble) 47 (1997), 915-928. (1997) Zbl0873.32025MR1465791
  9. Pflug P., Youssfi E.H., The Lu Qi-Keng conjecture fails for strongly convex algebraic domains, Arch. Math. 71 (1998), 240-245. (1998) Zbl0911.32037MR1637386
  10. Skwarczynski M., Biholomorphic invariants related to the Bergman function, Dissertationes Math. 173 (1980). (1980) Zbl0443.32014MR0575756

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