The Zeros of the Bergman Kernel for Some Reinhardt Domains
We consider the Reinhardt domain Dn={(ζ,z)∈C×Cn:|ζ|2<(1-|z1|2)⋯(1-|zn|2)}. We express the explicit closed form of the Bergman kernel for Dn using the exponential generating function for the Stirling number of the second kind. As an application, we show that the Bergman kernel Kn for Dn has zeros...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/3856096 |
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| author | Jong-Do Park |
| author_facet | Jong-Do Park |
| author_sort | Jong-Do Park |
| collection | DOAJ |
| description | We consider the Reinhardt domain Dn={(ζ,z)∈C×Cn:|ζ|2<(1-|z1|2)⋯(1-|zn|2)}. We express the explicit closed form of the Bergman kernel for Dn using the exponential generating function for the Stirling number of the second kind. As an application, we show that the Bergman kernel Kn for Dn has zeros if and only if n≥3. The study of the zeros of Kn is reduced to some real polynomial with coefficients which are related to Bernoulli numbers. This result is a complete characterization of the existence of zeros of the Bergman kernel for Dn for all positive integers n. |
| format | Article |
| id | doaj-art-ec358c5885e14fbc8b1961ba74ef1ce5 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-ec358c5885e14fbc8b1961ba74ef1ce52025-02-03T05:57:10ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/38560963856096The Zeros of the Bergman Kernel for Some Reinhardt DomainsJong-Do Park0Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Republic of KoreaWe consider the Reinhardt domain Dn={(ζ,z)∈C×Cn:|ζ|2<(1-|z1|2)⋯(1-|zn|2)}. We express the explicit closed form of the Bergman kernel for Dn using the exponential generating function for the Stirling number of the second kind. As an application, we show that the Bergman kernel Kn for Dn has zeros if and only if n≥3. The study of the zeros of Kn is reduced to some real polynomial with coefficients which are related to Bernoulli numbers. This result is a complete characterization of the existence of zeros of the Bergman kernel for Dn for all positive integers n.http://dx.doi.org/10.1155/2016/3856096 |
| spellingShingle | Jong-Do Park The Zeros of the Bergman Kernel for Some Reinhardt Domains Journal of Function Spaces |
| title | The Zeros of the Bergman Kernel for Some Reinhardt Domains |
| title_full | The Zeros of the Bergman Kernel for Some Reinhardt Domains |
| title_fullStr | The Zeros of the Bergman Kernel for Some Reinhardt Domains |
| title_full_unstemmed | The Zeros of the Bergman Kernel for Some Reinhardt Domains |
| title_short | The Zeros of the Bergman Kernel for Some Reinhardt Domains |
| title_sort | zeros of the bergman kernel for some reinhardt domains |
| url | http://dx.doi.org/10.1155/2016/3856096 |
| work_keys_str_mv | AT jongdopark thezerosofthebergmankernelforsomereinhardtdomains AT jongdopark zerosofthebergmankernelforsomereinhardtdomains |