| Title:
|
Zeroes of the Bergman kernel of Hartogs domains (English) |
| Author:
|
Engliš, Miroslav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
199-202 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Lu Qi-Keng conjecture |
| Keyword:
|
Hartogs domain |
| Keyword:
|
Bergman kernel |
| MSC:
|
32A07 |
| MSC:
|
32A25 |
| MSC:
|
32H10 |
| idZBL:
|
Zbl 1038.32002 |
| idMR:
|
MR1756941 |
| . |
| Date available:
|
2009-01-08T19:00:15Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119155 |
| . |
| Reference:
|
[B1] Boas H.P.: Counterexample to the Lu Qi-Keng conjecture.Proc. Amer. Math. Soc. 97 (1986), 374-375. Zbl 0596.32032, MR 0835902 |
| Reference:
|
[B2] Boas H.P.: The Lu Qi-Keng conjecture fails generically.Proc. Amer. Math. Soc. 124 (1996), 2021-2027. Zbl 0857.32010, MR 1317032 |
| Reference:
|
[BFS] Boas H.P., Fu S., Straube E.: The Bergman kernel function: explicit formulas and zeroes.Proc. Amer. Math. Soc. 127 (1999), 805-811. Zbl 0919.32013, MR 1469401 |
| Reference:
|
[E1] Engliš M.: Asymptotic behaviour of reproducing kernels of weighted Bergman spaces.Trans. Amer. Math. Soc. 349 (1997), 3717-3735. MR 1401769 |
| Reference:
|
[E2] Engliš M.: A Forelli-Rudin construction and asymptotics of weighted Bergman kernels.preprint, 1998. MR 1795632 |
| Reference:
|
[Lig] Ligocka E.: On the Forelli-Rudin construction and weighted Bergman projections.Studia Math. 94 (1989), 257-272. Zbl 0688.32020, MR 1019793 |
| Reference:
|
[Lu] Lu Q.-K. (K.H. Look): On Kaehler manifolds with constant curvature.Chinese Math. 8 (1966), 283-298. MR 0206990 |
| Reference:
|
[OPY] Oeljeklaus K., Pflug P., Youssfi E.H.: The Bergman kernel of the minimal ball and applications.Ann. Inst. Fourier (Grenoble) 47 (1997), 915-928. Zbl 0873.32025, MR 1465791 |
| Reference:
|
[PY] Pflug P., Youssfi E.H.: The Lu Qi-Keng conjecture fails for strongly convex algebraic domains.Arch. Math. 71 (1998), 240-245. Zbl 0911.32037, MR 1637386 |
| Reference:
|
[Skw] Skwarczynski M.: Biholomorphic invariants related to the Bergman function.Dissertationes Math. 173 (1980). Zbl 0443.32014, MR 0575756 |
| . |
