Zeroes of the Bergman kernel of Hartogs domains
Engliš, Miroslav
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000), p. 199-202 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2000-01-01
Classification:  32A07,  32A25,  32H10 
@article{119155,
     author = {Miroslav Engli\v s},
     title = {Zeroes of the Bergman kernel of Hartogs domains},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {41},
     year = {2000},
     pages = {199-202},
     zbl = {1038.32002},
     mrnumber = {1756941},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119155}
}

Engliš, Miroslav. Zeroes of the Bergman kernel of Hartogs domains. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 199-202. http://gdmltest.u-ga.fr/item/119155/

Boas H.P. Counterexample to the Lu Qi-Keng conjecture, Proc. Amer. Math. Soc. 97 (1986), 374-375. (1986) | MR 0835902 | Zbl 0596.32032

Boas H.P. The Lu Qi-Keng conjecture fails generically, Proc. Amer. Math. Soc. 124 (1996), 2021-2027. (1996) | MR 1317032 | Zbl 0857.32010

Boas H.P.; Fu S.; Straube E. The Bergman kernel function: explicit formulas and zeroes, Proc. Amer. Math. Soc. 127 (1999), 805-811. (1999) | MR 1469401 | Zbl 0919.32013

Engliš M. Asymptotic behaviour of reproducing kernels of weighted Bergman spaces, Trans. Amer. Math. Soc. 349 (1997), 3717-3735. (1997) | MR 1401769

Engliš M. A Forelli-Rudin construction and asymptotics of weighted Bergman kernels, preprint, 1998. | MR 1795632

Ligocka E. On the Forelli-Rudin construction and weighted Bergman projections, Studia Math. 94 (1989), 257-272. (1989) | MR 1019793 | Zbl 0688.32020

Lu Q.-K. (K.H. Look) On Kaehler manifolds with constant curvature, Chinese Math. 8 (1966), 283-298. (1966) | MR 0206990

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) | MR 1465791 | Zbl 0873.32025

Pflug P.; Youssfi E.H. The Lu Qi-Keng conjecture fails for strongly convex algebraic domains, Arch. Math. 71 (1998), 240-245. (1998) | MR 1637386 | Zbl 0911.32037

Skwarczynski M. Biholomorphic invariants related to the Bergman function, Dissertationes Math. 173 (1980). (1980) | MR 0575756 | Zbl 0443.32014